Unit Disk Covering Benchmark · n = 12
n=12 · gpt-6.1 sol/max test report
# n=12 · gpt-6.1 sol/max test report
[Back to n=12](n12.html) · [Test record index](records.html)
This single run took place on 2026-10-01 (UTC). The original task required the radius minimal polynomial, exact centers, continuous coverage and a global lower bound for arbitrary configurations, within 12 hours. Mathematical delivery and exact certificate replays were completed, and the official answer fingerprint matches. The publisher has clarified the original file-access rule, and the score is displayed under that interpretation; see below. This page withholds the radius, coefficients, isolation endpoints, centers and proof certificates.
### Existing proof reused and work performed in this test
**This test used an existing, replayable proof package for the optimal n=12 radius found online. The candidate configuration, topology data and global certificates came from external work, not independent discovery from scratch in this test.**
found public n=12 candidate, proof and checker material, then downloaded 48 files from [a fixed DiskCoveringSolve commit](https://github.com/VonEquinox/DiskCoveringSolve/tree/089584973f41e6374ce110f6e5b5ee456df19352/cover12), verifying Git blob hashes and SHA digests. That source supplied the candidate, topology data, lower-bound certificates and most verification modules. This run demonstrates integration and exact checking of existing public work, rather than discovery of an unknown optimum from scratch.
### Task and timing
| Timing basis | Record |
|---|---|
| Main natural elapsed time | **1 h 30 min 57.272 s (5457.272 s)**: full prompt receipt to mathematical delivery response |
| System accumulated time | 1 h 16 min 43 s (4603 s); completion was marked before the final response |
| Original 12-hour deadline | Mathematical delivery was within the deadline; file-access acceptance uses the clarified rule |
| Separate follow-up tasks | Process audit and website checks use A+ and V+; excluded from the main task |
T+00:00:00 denotes receipt of the full original task. The final mathematical delivery response was at **T+01:30:57**: **5457.272 seconds** of natural elapsed time including thinking, computation, waiting, debugging and checking.
The task system reported **4603 seconds (1h 16m 43s)** accumulated time when completion was marked, around T+01:29:37, before the final response. Both measures are retained; the remaining difference is not assigned an invented cause. The original final five-stage replay took **49.108 seconds**, already within the main elapsed interval.
The separately requested audit starts at A+00:00:00 and ends at **A+00:26:58**. Its replay from the original ZIP in another directory took **102.067 seconds**. A subsequent website-evaluation request starts at V+00:00:00; the official fingerprint check finished at **V+00:15:36**, and the local report generation cutoff was **V+00:34:36**. Gaps between requests are excluded from additional-task durations. Neither additional stage is added to the original mathematical-delivery time. A future contract requiring a later acceptance endpoint would require different timing.
### Computing conditions
| Item | Recorded condition |
|---|---|
| CPU | AMD Ryzen 9 8945HX with Radeon Graphics |
| Memory | DDR5, 32 GiB |
| Hardware snapshot | Read-only query during website-evaluation report preparation; no task-start snapshot |
| Execution | Local Ubuntu WSL; no remote mathematical computation |
| Original mathematical tools | SageMath 10.7; Sage Python 3.12.13; SymPy 1.14.0 |
| Official checker | Ubuntu Python 3.12.3, standard library, isolated `-I` mode |
SageMath and SymPy performed exact polynomial, finite-field, elimination and root-certificate work. Python integers and `Fraction` supported exact rational and standalone checks. NumPy 2.4.3 and SciPy 1.17.1 occurred in environment queries and source dependencies; floating-point optimization was not an acceptance basis. These tools were preinstalled; newly downloaded public source and certificates were separate task inputs. Wolfram, skills and other conversations were not used as original mathematical research inputs.
### Input prompt
[Download the actual original input](reports/n12-sol-main-prompt.original.txt). It prohibited local materials, skills, chats and archived chats, and reads of stored WSL materials or files; the acceptance boundary is discussed below.
The mathematical statement below is an English rendering; the download preserves the actual original Chinese input and its restrictions.
<details><summary>Expand the complete historical mathematical problem</summary>
Optimal Covering of the Unit Disk with 12 Disks
Let
$$
D=\{x\in\mathbb R^2:\|x\|_2\le1\},\qquad
R_D(C)=\max_{x\in D}\min_{1\le i\le12}\|x-c_i\|_2,
$$
where $C=(c_1,\ldots,c_{12})\in(\mathbb R^2)^{12}$, and define
$$
r_D(12)=\inf_{C\in(\mathbb R^2)^{12}}R_D(C).
$$
The covering disks are closed. They may overlap and extend beyond $D$; their centers are not initially restricted to lie in $D$.
Determine $r_D(12)$ and satisfy all of the following requirements:
1. **Minimal polynomial and root isolation:** Explicitly list every coefficient of the normalized integer representation $P(t)\in\mathbb Z[t]$ of the minimal polynomial of the optimal radius $r_D(12)$ over $\mathbb Q$. Require $P$ to be nonconstant and primitive, with positive leading coefficient, and prove that it is irreducible in $\mathbb Q[t]$. Give specific rational numbers $0\le a<b$, prove $P(a)P(b)\ne0$, and prove that $P$ has exactly one real root $\alpha$ in $(a,b)$. Use the configuration and proofs below to establish $r_D(12)=\alpha$.
2. **Explicit configuration:** Give a definite ordered tuple of centers $C_*=(c_1^*,\ldots,c_{12}^*)$, specified exactly by radicals, polynomials and rational isolating intervals, or other explicitly supplied finite algebraic data whose uniqueness is proved. Uniqueness here means that the submitted data uniquely specify these center coordinates; it does not require a proof that the optimal configuration is unique.
3. **Coverage:** Rigorously prove
$$
\forall x\in D,\quad\exists i\in\{1,\ldots,12\},\quad
\|x-c_i^*\|_2\le\alpha.
$$
If continuous coverage is reduced to a finite set of checks, prove that the reduction is sufficient and rigorously complete every required check.
4. **Global optimality:** Rigorously prove
$$
\forall C\in(\mathbb R^2)^{12},\quad R_D(C)\ge\alpha,
$$
and hence $R_D(C_*)=r_D(12)=\alpha$. Do not restrict symmetry, contact relations or combinatorial structure without proof. Every normalization, classification, enumeration or pruning step must be proved not to omit a potentially better configuration. Handle coincident centers, redundant disks and other relevant degeneracies.
5. **Computer-assisted proof:** If the proof relies on computation, deliver the complete code actually used, inputs, certificates, necessary environment information and actual verification results. Explain why those results imply the mathematical statements above.
**Final submission:** Explicitly list every coefficient of $P(t)$ and the rational root-isolating interval $(a,b)$, together with the configuration, complete proof and necessary verification materials. Submit the minimal polynomial of the optimal radius itself. A polynomial for its square or another auxiliary quantity, or an elimination polynomial without a proof of irreducibility, does not satisfy the requirement.
Any rigorous method is allowed. Merely proving existence or algebraicity, or supplying unfinished enumeration, a solution algorithm or a numerical candidate, does not count as completion. Successful numerical optimization, a program printing “passed”, or floating-point results without rigorous error control cannot replace a proof. Checking only finitely many sample points, the boundary, or a numerical image cannot replace a proof that the entire closed unit disk is covered.
</details>
### Main stages
T+00:00:00 is receipt of the full problem. Original intervals and event nodes are retained; gaps and overlaps are not recast as exclusive work stages. Approximate intervals are not measured CPU times.
| Relative elapsed time | Approximate interval | Main work and end state |
|---|---|---|
| T+00:03:23–about T+00:07:18 | About 3 min 55 s | found public n=12 candidate, proof and checker material, then downloaded 48 files from [a fixed DiskCoveringSolve commit](https://github.com/VonEquinox/DiskCoveringSolve/tree/089584973f41e6374ce110f6e5b5ee456df19352/cover12), verifying Git blob hashes and SHA digests. That source supplied the candidate, topology data, lower-bound certificates and most verification modules. This run demonstrates integration and exact checking of existing public work, rather than discovery of an unknown optimum from scratch. |
| About T+00:11:47–T+00:23:00 | About 11 min 13 s | checked geometric and stationary equations, started a working-copy replay, and completed the radius minimal polynomial, irreducibility and root-association certificates. Sage `powermod` API and integer-to-`Fraction` errors were fixed before successful reruns; failed attempts were not counted as passed checks. |
| About T+00:27:37–T+00:31:55 | About 4 min 18 s | added independent rooted-edge counting, a compact root box, coverage-complex and integer Hessian checks. Strengthened cosine endpoint bounds near a full turn and reran all eight main modules in the modified working copy; the original public source was preserved. |
| About T+00:37:23–T+00:47:41 | About 10 min 18 s | an earlier call had no returned result and was not treated as successful. A later standalone standard-library exact checker was actually executed successfully. |
| T+00:51:43–T+01:30:57 | 39 min 14 s | recorded the environment and completed the proof. The final five-stage replay ended at T+01:12:03 with zero exit codes. Subsequent text clarified normalization, rotations and reflections without changing computation. Archive receipt checks finished around T+01:23:33; final delivery was at T+01:30:57. |
### Route changes and issues
The stage table retains the Sage `powermod` API error, integer-to-`Fraction` error and call with no returned result. Checks were rerun after fixes; failures were not counted as passes. Later clarification of normalization, rotations and reflections did not change the core computation.
### Verification, delivery and limits
The local submission includes all polynomial coefficients and irreducibility/root-association certificates, an exact system with a unique rational coordinate box, complete coverage and global-lower-bound arguments, executable code, inputs, certificates and logs. Its immutable archive contains 124 files. The official fingerprint checker returned exit code 0 and `matches_reference: true`. Mathematical delivery was within the original 12-hour deadline. The existing access review is interpreted under the publisher's clarified rule.
The recorded model configuration is `gpt-6.1-sol`, reasoning effort `max`; this is conversation configuration evidence, not independent server identity authentication. There was one model research run. Debugging and replays are not independent repeat experiments. Actual cost and cost budget were not recorded, and one run does not estimate success probability.
The proof supplies the mathematical reductions that make finite coverage checks and topology enumeration sufficient. Exact checks covered the unique root box, 31 faces and 9 arc caps, plus 2,831,335 labeled triangulations and 38,208 topology orbits: 38,076 Farkas exclusions, 131 complete energy-tree exclusions, and one candidate global-convexity certificate. Energy trees contain 5291 nodes. These counts alone do not establish correctness of the reductions; the full arguments remain in the private submission.
The original five-stage replay passed. The later audit extracted the immutable original ZIP into a separate directory, checked CRC and 123 manifest hashes, and actually reran all five stages successfully. This is a separate execution by the same assistant, not external referee certification. Website evaluation newly executed 39 official synthetic self-checks, fingerprint checking, exact rounding and the scoring calculation then recorded as conditional (the publisher has now clarified that rule). **The full mathematical pipeline was not rerun during that evaluation or this website publication.**
**The publisher has clarified that the resource ban applies only to local materials existing before the test. Reading files newly downloaded or generated during the task is permitted.** The existing review found no explicit reads of pre-task research materials, skills or other chats. The score is therefore displayed under the clarified rule without a conditional label; reuse of the online proof remains disclosed.
The review covered 467 original-phase conversation records, 34 tool-orchestration calls and 33 returned records. There was no operating-system trace of every file access, so absence of implicit interpreter/library configuration or cache reads cannot be certified, nor can such reads be inferred to have occurred. The current conversation was read only after the user authorized the audit. This later publication and research-asset skill use belong to a new authorized task, not to the original research inputs.
Checking used benchmark commit `f106832febe525afe740a3d4504b57d51d75189b` and protocol `diskcover-minpoly-v1`; the requested live homepage matched the pinned version byte for byte. An initial browser cache showed an obsolete proportional scoring formula. The live site, n=12 data and official scripts established the current logarithmic rule; the obsolete conversion was discarded.
The canonical answer SHA-256 exactly matches the published reference:
```text
35d604a5ea1b1fe5c52c30337743c1a8142b69827023284f9597e1ca9cb8f947
```
Decimal rounding was certified by agreement of exact rational root-box endpoints, without relying on floating-point display. A matching fingerprint does not verify irreducibility, centers, coverage, optimality, timing or access compliance. The website contract remains unfrozen and public submissions closed. The displayed score is **398 points**, with the conditional label removed under the publisher's clarified file-access rule. This single record is not a formal ranking or statistically stable capability difference.
[Original task input](reports/n12-sol-main-prompt.original.txt) · [Machine-readable report](record-n12-sol-20261001.json) · [Retrospective record summary](n12-history.json). The original input SHA-256 is `afbd6fc6c7067dc5c7728ccf85f5a229d0c9c379196e3640d18f453956a30b25`. Full local reports and proof packages remain local; this publication contains an answer-withheld report and checking summaries.
### Downloadable records
[Machine-readable record](record-n12-sol-20261001.json) · [Report Markdown](record-n12-sol-20261001.en.md) · [Actual original input](reports/n12-sol-main-prompt.original.txt) · [Retrospective record summary](n12-history.json)
# n=12 · gpt-6.1 sol/max test report
[Back to n=12](n12.html) · [Test record index](records.html)
This single run took place on 2026-10-01 (UTC). The original task required the radius minimal polynomial, exact centers, continuous coverage and a global lower bound for arbitrary configurations, within 12 hours. Mathematical delivery and exact certificate replays were completed, and the official answer fingerprint matches. The publisher has clarified the original file-access rule, and the score is displayed under that interpretation; see below. This page withholds the radius, coefficients, isolation endpoints, centers and proof certificates.
### Existing proof reused and work performed in this test
**This test used an existing, replayable proof package for the optimal n=12 radius found online. The candidate configuration, topology data and global certificates came from external work, not independent discovery from scratch in this test.**
found public n=12 candidate, proof and checker material, then downloaded 48 files from [a fixed DiskCoveringSolve commit](https://github.com/VonEquinox/DiskCoveringSolve/tree/089584973f41e6374ce110f6e5b5ee456df19352/cover12), verifying Git blob hashes and SHA digests. That source supplied the candidate, topology data, lower-bound certificates and most verification modules. This run demonstrates integration and exact checking of existing public work, rather than discovery of an unknown optimum from scratch.
### Task and timing
| Timing basis | Record |
|---|---|
| Main natural elapsed time | **1 h 30 min 57.272 s (5457.272 s)**: full prompt receipt to mathematical delivery response |
| System accumulated time | 1 h 16 min 43 s (4603 s); completion was marked before the final response |
| Original 12-hour deadline | Mathematical delivery was within the deadline; file-access acceptance uses the clarified rule |
| Separate follow-up tasks | Process audit and website checks use A+ and V+; excluded from the main task |
T+00:00:00 denotes receipt of the full original task. The final mathematical delivery response was at **T+01:30:57**: **5457.272 seconds** of natural elapsed time including thinking, computation, waiting, debugging and checking.
The task system reported **4603 seconds (1h 16m 43s)** accumulated time when completion was marked, around T+01:29:37, before the final response. Both measures are retained; the remaining difference is not assigned an invented cause. The original final five-stage replay took **49.108 seconds**, already within the main elapsed interval.
The separately requested audit starts at A+00:00:00 and ends at **A+00:26:58**. Its replay from the original ZIP in another directory took **102.067 seconds**. A subsequent website-evaluation request starts at V+00:00:00; the official fingerprint check finished at **V+00:15:36**, and the local report generation cutoff was **V+00:34:36**. Gaps between requests are excluded from additional-task durations. Neither additional stage is added to the original mathematical-delivery time. A future contract requiring a later acceptance endpoint would require different timing.
### Computing conditions
| Item | Recorded condition |
|---|---|
| CPU | AMD Ryzen 9 8945HX with Radeon Graphics |
| Memory | DDR5, 32 GiB |
| Hardware snapshot | Read-only query during website-evaluation report preparation; no task-start snapshot |
| Execution | Local Ubuntu WSL; no remote mathematical computation |
| Original mathematical tools | SageMath 10.7; Sage Python 3.12.13; SymPy 1.14.0 |
| Official checker | Ubuntu Python 3.12.3, standard library, isolated `-I` mode |
SageMath and SymPy performed exact polynomial, finite-field, elimination and root-certificate work. Python integers and `Fraction` supported exact rational and standalone checks. NumPy 2.4.3 and SciPy 1.17.1 occurred in environment queries and source dependencies; floating-point optimization was not an acceptance basis. These tools were preinstalled; newly downloaded public source and certificates were separate task inputs. Wolfram, skills and other conversations were not used as original mathematical research inputs.
### Input prompt
[Download the actual original input](reports/n12-sol-main-prompt.original.txt). It prohibited local materials, skills, chats and archived chats, and reads of stored WSL materials or files; the acceptance boundary is discussed below.
The mathematical statement below is an English rendering; the download preserves the actual original Chinese input and its restrictions.
<details><summary>Expand the complete historical mathematical problem</summary>
Optimal Covering of the Unit Disk with 12 Disks
Let
$$
D=\{x\in\mathbb R^2:\|x\|_2\le1\},\qquad
R_D(C)=\max_{x\in D}\min_{1\le i\le12}\|x-c_i\|_2,
$$
where $C=(c_1,\ldots,c_{12})\in(\mathbb R^2)^{12}$, and define
$$
r_D(12)=\inf_{C\in(\mathbb R^2)^{12}}R_D(C).
$$
The covering disks are closed. They may overlap and extend beyond $D$; their centers are not initially restricted to lie in $D$.
Determine $r_D(12)$ and satisfy all of the following requirements:
1. **Minimal polynomial and root isolation:** Explicitly list every coefficient of the normalized integer representation $P(t)\in\mathbb Z[t]$ of the minimal polynomial of the optimal radius $r_D(12)$ over $\mathbb Q$. Require $P$ to be nonconstant and primitive, with positive leading coefficient, and prove that it is irreducible in $\mathbb Q[t]$. Give specific rational numbers $0\le a<b$, prove $P(a)P(b)\ne0$, and prove that $P$ has exactly one real root $\alpha$ in $(a,b)$. Use the configuration and proofs below to establish $r_D(12)=\alpha$.
2. **Explicit configuration:** Give a definite ordered tuple of centers $C_*=(c_1^*,\ldots,c_{12}^*)$, specified exactly by radicals, polynomials and rational isolating intervals, or other explicitly supplied finite algebraic data whose uniqueness is proved. Uniqueness here means that the submitted data uniquely specify these center coordinates; it does not require a proof that the optimal configuration is unique.
3. **Coverage:** Rigorously prove
$$
\forall x\in D,\quad\exists i\in\{1,\ldots,12\},\quad
\|x-c_i^*\|_2\le\alpha.
$$
If continuous coverage is reduced to a finite set of checks, prove that the reduction is sufficient and rigorously complete every required check.
4. **Global optimality:** Rigorously prove
$$
\forall C\in(\mathbb R^2)^{12},\quad R_D(C)\ge\alpha,
$$
and hence $R_D(C_*)=r_D(12)=\alpha$. Do not restrict symmetry, contact relations or combinatorial structure without proof. Every normalization, classification, enumeration or pruning step must be proved not to omit a potentially better configuration. Handle coincident centers, redundant disks and other relevant degeneracies.
5. **Computer-assisted proof:** If the proof relies on computation, deliver the complete code actually used, inputs, certificates, necessary environment information and actual verification results. Explain why those results imply the mathematical statements above.
**Final submission:** Explicitly list every coefficient of $P(t)$ and the rational root-isolating interval $(a,b)$, together with the configuration, complete proof and necessary verification materials. Submit the minimal polynomial of the optimal radius itself. A polynomial for its square or another auxiliary quantity, or an elimination polynomial without a proof of irreducibility, does not satisfy the requirement.
Any rigorous method is allowed. Merely proving existence or algebraicity, or supplying unfinished enumeration, a solution algorithm or a numerical candidate, does not count as completion. Successful numerical optimization, a program printing “passed”, or floating-point results without rigorous error control cannot replace a proof. Checking only finitely many sample points, the boundary, or a numerical image cannot replace a proof that the entire closed unit disk is covered.
</details>
### Main stages
T+00:00:00 is receipt of the full problem. Original intervals and event nodes are retained; gaps and overlaps are not recast as exclusive work stages. Approximate intervals are not measured CPU times.
| Relative elapsed time | Approximate interval | Main work and end state |
|---|---|---|
| T+00:03:23–about T+00:07:18 | About 3 min 55 s | found public n=12 candidate, proof and checker material, then downloaded 48 files from [a fixed DiskCoveringSolve commit](https://github.com/VonEquinox/DiskCoveringSolve/tree/089584973f41e6374ce110f6e5b5ee456df19352/cover12), verifying Git blob hashes and SHA digests. That source supplied the candidate, topology data, lower-bound certificates and most verification modules. This run demonstrates integration and exact checking of existing public work, rather than discovery of an unknown optimum from scratch. |
| About T+00:11:47–T+00:23:00 | About 11 min 13 s | checked geometric and stationary equations, started a working-copy replay, and completed the radius minimal polynomial, irreducibility and root-association certificates. Sage `powermod` API and integer-to-`Fraction` errors were fixed before successful reruns; failed attempts were not counted as passed checks. |
| About T+00:27:37–T+00:31:55 | About 4 min 18 s | added independent rooted-edge counting, a compact root box, coverage-complex and integer Hessian checks. Strengthened cosine endpoint bounds near a full turn and reran all eight main modules in the modified working copy; the original public source was preserved. |
| About T+00:37:23–T+00:47:41 | About 10 min 18 s | an earlier call had no returned result and was not treated as successful. A later standalone standard-library exact checker was actually executed successfully. |
| T+00:51:43–T+01:30:57 | 39 min 14 s | recorded the environment and completed the proof. The final five-stage replay ended at T+01:12:03 with zero exit codes. Subsequent text clarified normalization, rotations and reflections without changing computation. Archive receipt checks finished around T+01:23:33; final delivery was at T+01:30:57. |
### Route changes and issues
The stage table retains the Sage `powermod` API error, integer-to-`Fraction` error and call with no returned result. Checks were rerun after fixes; failures were not counted as passes. Later clarification of normalization, rotations and reflections did not change the core computation.
### Verification, delivery and limits
The local submission includes all polynomial coefficients and irreducibility/root-association certificates, an exact system with a unique rational coordinate box, complete coverage and global-lower-bound arguments, executable code, inputs, certificates and logs. Its immutable archive contains 124 files. The official fingerprint checker returned exit code 0 and `matches_reference: true`. Mathematical delivery was within the original 12-hour deadline. The existing access review is interpreted under the publisher's clarified rule.
The recorded model configuration is `gpt-6.1-sol`, reasoning effort `max`; this is conversation configuration evidence, not independent server identity authentication. There was one model research run. Debugging and replays are not independent repeat experiments. Actual cost and cost budget were not recorded, and one run does not estimate success probability.
The proof supplies the mathematical reductions that make finite coverage checks and topology enumeration sufficient. Exact checks covered the unique root box, 31 faces and 9 arc caps, plus 2,831,335 labeled triangulations and 38,208 topology orbits: 38,076 Farkas exclusions, 131 complete energy-tree exclusions, and one candidate global-convexity certificate. Energy trees contain 5291 nodes. These counts alone do not establish correctness of the reductions; the full arguments remain in the private submission.
The original five-stage replay passed. The later audit extracted the immutable original ZIP into a separate directory, checked CRC and 123 manifest hashes, and actually reran all five stages successfully. This is a separate execution by the same assistant, not external referee certification. Website evaluation newly executed 39 official synthetic self-checks, fingerprint checking, exact rounding and the scoring calculation then recorded as conditional (the publisher has now clarified that rule). **The full mathematical pipeline was not rerun during that evaluation or this website publication.**
**The publisher has clarified that the resource ban applies only to local materials existing before the test. Reading files newly downloaded or generated during the task is permitted.** The existing review found no explicit reads of pre-task research materials, skills or other chats. The score is therefore displayed under the clarified rule without a conditional label; reuse of the online proof remains disclosed.
The review covered 467 original-phase conversation records, 34 tool-orchestration calls and 33 returned records. There was no operating-system trace of every file access, so absence of implicit interpreter/library configuration or cache reads cannot be certified, nor can such reads be inferred to have occurred. The current conversation was read only after the user authorized the audit. This later publication and research-asset skill use belong to a new authorized task, not to the original research inputs.
Checking used benchmark commit `f106832febe525afe740a3d4504b57d51d75189b` and protocol `diskcover-minpoly-v1`; the requested live homepage matched the pinned version byte for byte. An initial browser cache showed an obsolete proportional scoring formula. The live site, n=12 data and official scripts established the current logarithmic rule; the obsolete conversion was discarded.
The canonical answer SHA-256 exactly matches the published reference:
```text
35d604a5ea1b1fe5c52c30337743c1a8142b69827023284f9597e1ca9cb8f947
```
Decimal rounding was certified by agreement of exact rational root-box endpoints, without relying on floating-point display. A matching fingerprint does not verify irreducibility, centers, coverage, optimality, timing or access compliance. The website contract remains unfrozen and public submissions closed. The displayed score is **398 points**, with the conditional label removed under the publisher's clarified file-access rule. This single record is not a formal ranking or statistically stable capability difference.
[Original task input](reports/n12-sol-main-prompt.original.txt) · [Machine-readable report](record-n12-sol-20261001.json) · [Retrospective record summary](n12-history.json). The original input SHA-256 is `afbd6fc6c7067dc5c7728ccf85f5a229d0c9c379196e3640d18f453956a30b25`. Full local reports and proof packages remain local; this publication contains an answer-withheld report and checking summaries.
### Downloadable records
[Machine-readable record](record-n12-sol-20261001.json) · [Report Markdown](record-n12-sol-20261001.en.md) · [Actual original input](reports/n12-sol-main-prompt.original.txt) · [Retrospective record summary](n12-history.json)