Unit Disk Covering Benchmark · n = 12
n=12 · gpt-6 astra/max test report
# n=12 · gpt-6 astra/max test report
[Back to n=12](n12.html) · [Test record index](records.html)
Test date: 2026-10-01. Model: **gpt-6 astra/max**. One run. This is a post-hoc self-test of an existing research run, not a formal ranking under a frozen contract. Mathematical answers, exact centers, full proof materials and private chats are withheld.
### 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.**
The run used existing configurations, topology data and certificates from the [pinned VonEquinox/DiskCoveringSolve commit](https://github.com/VonEquinox/DiskCoveringSolve/tree/089584973f41e6374ce110f6e5b5ee456df19352/cover12). Added work included reviewing reductions and replaying certificates, independent counting, strengthened exact interval and input checks, and elimination, irreducibility and root isolation for the radius's minimal polynomial. **This was not a from-scratch discovery of the configuration or all global certificates.**
### Task and timing
| Timing basis | Record |
|---|---|
| Main natural elapsed time | **52 min 55.402 s (3175.402 s)**: full problem receipt to fully recorded final response |
| System accumulated time | 45 min 5 s (2705 s): later start and earlier endpoint; not a substitute for elapsed time |
| Original 12-hour deadline | Mathematical delivery was within the deadline; only pre-task local materials are prohibited |
| Separate process audit | 16 min 37.186 s; excluded from the main task |
| Separate website validation and report | 29 min 7.02885 s; excluded from the main task |
The primary interval starts when the first complete problem was received at **T+00:00:00** and ends when the final response was fully recorded at **T+00:52:55**: exactly **3175.402 seconds (52 minutes 55.402 seconds)**. It includes retrieval, computation, waiting, verification and submission. Waiting was not deducted.
The Goal counter was 2705 seconds (45 minutes 5 seconds), with a later start and earlier endpoint. It cannot replace the primary interval; the original response's description of it as total time is corrected here. The original final three-stage program took about 124.96 seconds, and its later audit replay about 215.91 seconds. Neither is total task time.
The separately requested process audit took 16 minutes 37.186 seconds. Subsequent website validation and report preparation took 29 minutes 7.02885 seconds through that report's checking cutoff. These follow-ups and gaps between tasks are excluded from the original submission interval.
### Computing conditions
| Field | Recorded information |
|---|---|
| Solver and reasoning | gpt-6-astra / max, from original solver metadata |
| Agents and repetitions | No subagents in the original solve; one run; replay is not another independent solve |
| CPU | AMD Ryzen 9 8945HX with Radeon Graphics |
| Physical memory | DDR5, 32 GiB; 34359738368 bytes |
| Hardware scope | Queried while preparing the report, not a frozen opening snapshot |
| Execution environment | Local Ubuntu WSL2; Python 3.12.3; Linux kernel 6.6.87.2 |
| Newly installed libraries | SymPy 1.14.0, NumPy 2.2.6, SciPy 1.15.3, mpmath 1.3.0 in a fresh environment |
| Exact computation | Elimination, symbolic identities, Sturm sequences, rational and interval certificate checks |
| Floating-point limits | Dependencies and summaries; optimization, summaries and images were not accepted as proofs |
| Sage / Wolfram | Not used; versions not queried |
| Time budget | 43200 seconds |
| Monetary budget / cost | Not recorded; null, not zero |
| Codex Goal cumulative counter | 319768; see the accounting definition below; not billed tokens or monetary cost |
The Codex Goal cumulative counter is a budget-accounting field of Codex's Goal feature, not an industry-standard total-token metric. The verified [Codex 0.159.2 implementation](https://github.com/openai/codex/blob/rust-v0.159.2/codex-rs/ext/goal/src/accounting.rs#L527-L532) accumulates usage increments as input tokens minus cached input tokens plus output tokens: uncached input plus output. Output already includes reasoning tokens, which must not be added again. Historical versions follow their own implementation. This field is not the whole-chat token total, billed-token usage or monetary cost, and must not be compared directly with another platform's total-token figure.
Memory type 34 (0x22) maps to DDR5 in the Memory Device Type table of [DMTF SMBIOS 3.4.0](https://www.dmtf.org/sites/default/files/standards/documents/DSP0134_3.4.0.pdf).
### Input prompt
The original problem required the optimal radius's irreducible primitive integer minimal polynomial, every coefficient, a rational isolating interval, exactly specified ordered centers, continuous coverage of the entire closed disk, a global lower bound over arbitrary configurations, and all code, inputs and certificates actually used. Numerical candidates, sampling and unfinished enumeration were insufficient. Centers outside the disk and degenerate configurations had to be handled.
[Download the actual mathematical problem input](reports/n12-astra-main-prompt.original.txt). Starting materials also included user-provided environment facts and the benchmark website URL. The opening benchmark commit and a separate opening hardware snapshot were not recorded. The original deadline was 12 hours.
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+00:04:31 | Point/start event; duration not recorded | Goal started; website and literature retrieval |
| About T+00:06 to 00:09 | About 3 min | Located numerical candidates and a public twelve-disk proof bundle; candidates alone were not treated as global proofs |
| About T+00:10 to 00:17 | About 7 min | Retrieved pinned code and certificates, checked provenance, prepared a fresh environment and inspected rational verification paths |
| From T+00:16:56 | Point/start event; duration not recorded | Started certificate verification and new symbolic elimination |
| About T+00:20 to 00:23 | About 3 min | Fixed symbolic-integer JSON serialization and repeated irreducibility and isolation checks |
| About T+00:25 to 00:36 | About 11 min | Added independent topology counting, input and complete-tree checks, interval bounds and a unique root box |
| About T+00:42 | Point/start event; duration not recorded | Completed the proof document, arbitrary-configuration reduction and continuous-coverage justification |
| T+00:43:15 to 00:45:20 | 2 min 5 s | Final algebra, scope and coverage verification stages all returned exit code 0 |
| About T+00:48 | Point/start event; duration not recorded | Packaging, per-file hashes and ZIP checks |
| T+00:49:35 | Point/start event; duration not recorded | Goal marked complete; not the final-response endpoint |
| T+00:52:55 | Point/start event; duration not recorded | Full final submission; primary endpoint |
### Route changes and issues
A temporary-path launch failed and symbolic-integer serialization failed; both were repaired and rechecked. Failed executions were not counted as successful. Later website-source retrieval encountered endpoint timeouts and API rate limiting after redundant requests; previously verified pinned files were used. Those events occurred after the original solve and do not affect its primary elapsed time.
### Verification, delivery and limits
Post-hoc validation used benchmark commit `f106832febe525afe740a3d4504b57d51d75189b` and protocol `diskcover-minpoly-v1`. The opening version was not recorded; this cannot be described as a pre-frozen contract. Publisher tools were actually executed:
| Check | Result and limit |
|---|---|
| tools/check_tools.py | 39 synthetic checks passed, exit 0; not mathematical problem solving |
| tools/diskcover_answer.py | matches_reference: true, exit 0; integers were not converted through floating point |
| n=12 reference fingerprint | Exact match |
| Original mathematical deliverables | Complete proof, code, inputs, certificates and logs submitted |
| Original solve and later audit copy | Three-stage replays passed; self-review of the same model's work |
| Independent external mathematical review | Not performed |
| This report stage | Public tools and rounding checks rerun; geometry verifier not rerun |
The public fingerprint is `35d604a5ea1b1fe5c52c30337743c1a8142b69827023284f9597e1ca9cb8f947`. Matching compares encoded answer data only; it does not prove minimality, irreducibility, continuous coverage, global optimality, timing authenticity or resource-rule compliance.
Prior proof checks included modular irreducibility, Sturm isolation, a unique root box, full-disk coverage via triangular faces and circular caps, and global topology classification with Farkas and energy-tree exclusions. The earlier statement that floating point was used only for display was too absolute: the summary layer also compares floating-point report values. Acceptance relies separately on rational, outward-interval and symbolic checks. Self-review did not replace those checks with floating-point summaries and is not external certification.
The problem page displays **477 points**. Scoring is explained on the [problem page](n12.html) and [testing guide](guide.html), rather than repeated here. The publisher has settled the resource-rule interpretation; this remains a single retrospective record, with public submissions closed and no frozen formal comparison contract.
**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 later report, archival and website publication use local reports and the user-selected skill under separate explicit authorization. They do not retroactively establish compliance of the original solve.
### Downloadable records
[Machine-readable record](record-n12-astra-20261001.json) · [Report Markdown](record-n12-astra-20261001.en.md) · [Actual original input](reports/n12-astra-main-prompt.original.txt)
[Download this record's structured JSON](record-n12-astra-20261001.json). This public version contains input, resources, relative chronology, sources, check summaries and acceptance limits, but no mathematical answers, proof bundles, private paths, billing data or full chats.
# n=12 · gpt-6 astra/max test report
[Back to n=12](n12.html) · [Test record index](records.html)
Test date: 2026-10-01. Model: **gpt-6 astra/max**. One run. This is a post-hoc self-test of an existing research run, not a formal ranking under a frozen contract. Mathematical answers, exact centers, full proof materials and private chats are withheld.
### 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.**
The run used existing configurations, topology data and certificates from the [pinned VonEquinox/DiskCoveringSolve commit](https://github.com/VonEquinox/DiskCoveringSolve/tree/089584973f41e6374ce110f6e5b5ee456df19352/cover12). Added work included reviewing reductions and replaying certificates, independent counting, strengthened exact interval and input checks, and elimination, irreducibility and root isolation for the radius's minimal polynomial. **This was not a from-scratch discovery of the configuration or all global certificates.**
### Task and timing
| Timing basis | Record |
|---|---|
| Main natural elapsed time | **52 min 55.402 s (3175.402 s)**: full problem receipt to fully recorded final response |
| System accumulated time | 45 min 5 s (2705 s): later start and earlier endpoint; not a substitute for elapsed time |
| Original 12-hour deadline | Mathematical delivery was within the deadline; only pre-task local materials are prohibited |
| Separate process audit | 16 min 37.186 s; excluded from the main task |
| Separate website validation and report | 29 min 7.02885 s; excluded from the main task |
The primary interval starts when the first complete problem was received at **T+00:00:00** and ends when the final response was fully recorded at **T+00:52:55**: exactly **3175.402 seconds (52 minutes 55.402 seconds)**. It includes retrieval, computation, waiting, verification and submission. Waiting was not deducted.
The Goal counter was 2705 seconds (45 minutes 5 seconds), with a later start and earlier endpoint. It cannot replace the primary interval; the original response's description of it as total time is corrected here. The original final three-stage program took about 124.96 seconds, and its later audit replay about 215.91 seconds. Neither is total task time.
The separately requested process audit took 16 minutes 37.186 seconds. Subsequent website validation and report preparation took 29 minutes 7.02885 seconds through that report's checking cutoff. These follow-ups and gaps between tasks are excluded from the original submission interval.
### Computing conditions
| Field | Recorded information |
|---|---|
| Solver and reasoning | gpt-6-astra / max, from original solver metadata |
| Agents and repetitions | No subagents in the original solve; one run; replay is not another independent solve |
| CPU | AMD Ryzen 9 8945HX with Radeon Graphics |
| Physical memory | DDR5, 32 GiB; 34359738368 bytes |
| Hardware scope | Queried while preparing the report, not a frozen opening snapshot |
| Execution environment | Local Ubuntu WSL2; Python 3.12.3; Linux kernel 6.6.87.2 |
| Newly installed libraries | SymPy 1.14.0, NumPy 2.2.6, SciPy 1.15.3, mpmath 1.3.0 in a fresh environment |
| Exact computation | Elimination, symbolic identities, Sturm sequences, rational and interval certificate checks |
| Floating-point limits | Dependencies and summaries; optimization, summaries and images were not accepted as proofs |
| Sage / Wolfram | Not used; versions not queried |
| Time budget | 43200 seconds |
| Monetary budget / cost | Not recorded; null, not zero |
| Codex Goal cumulative counter | 319768; see the accounting definition below; not billed tokens or monetary cost |
The Codex Goal cumulative counter is a budget-accounting field of Codex's Goal feature, not an industry-standard total-token metric. The verified [Codex 0.159.2 implementation](https://github.com/openai/codex/blob/rust-v0.159.2/codex-rs/ext/goal/src/accounting.rs#L527-L532) accumulates usage increments as input tokens minus cached input tokens plus output tokens: uncached input plus output. Output already includes reasoning tokens, which must not be added again. Historical versions follow their own implementation. This field is not the whole-chat token total, billed-token usage or monetary cost, and must not be compared directly with another platform's total-token figure.
Memory type 34 (0x22) maps to DDR5 in the Memory Device Type table of [DMTF SMBIOS 3.4.0](https://www.dmtf.org/sites/default/files/standards/documents/DSP0134_3.4.0.pdf).
### Input prompt
The original problem required the optimal radius's irreducible primitive integer minimal polynomial, every coefficient, a rational isolating interval, exactly specified ordered centers, continuous coverage of the entire closed disk, a global lower bound over arbitrary configurations, and all code, inputs and certificates actually used. Numerical candidates, sampling and unfinished enumeration were insufficient. Centers outside the disk and degenerate configurations had to be handled.
[Download the actual mathematical problem input](reports/n12-astra-main-prompt.original.txt). Starting materials also included user-provided environment facts and the benchmark website URL. The opening benchmark commit and a separate opening hardware snapshot were not recorded. The original deadline was 12 hours.
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+00:04:31 | Point/start event; duration not recorded | Goal started; website and literature retrieval |
| About T+00:06 to 00:09 | About 3 min | Located numerical candidates and a public twelve-disk proof bundle; candidates alone were not treated as global proofs |
| About T+00:10 to 00:17 | About 7 min | Retrieved pinned code and certificates, checked provenance, prepared a fresh environment and inspected rational verification paths |
| From T+00:16:56 | Point/start event; duration not recorded | Started certificate verification and new symbolic elimination |
| About T+00:20 to 00:23 | About 3 min | Fixed symbolic-integer JSON serialization and repeated irreducibility and isolation checks |
| About T+00:25 to 00:36 | About 11 min | Added independent topology counting, input and complete-tree checks, interval bounds and a unique root box |
| About T+00:42 | Point/start event; duration not recorded | Completed the proof document, arbitrary-configuration reduction and continuous-coverage justification |
| T+00:43:15 to 00:45:20 | 2 min 5 s | Final algebra, scope and coverage verification stages all returned exit code 0 |
| About T+00:48 | Point/start event; duration not recorded | Packaging, per-file hashes and ZIP checks |
| T+00:49:35 | Point/start event; duration not recorded | Goal marked complete; not the final-response endpoint |
| T+00:52:55 | Point/start event; duration not recorded | Full final submission; primary endpoint |
### Route changes and issues
A temporary-path launch failed and symbolic-integer serialization failed; both were repaired and rechecked. Failed executions were not counted as successful. Later website-source retrieval encountered endpoint timeouts and API rate limiting after redundant requests; previously verified pinned files were used. Those events occurred after the original solve and do not affect its primary elapsed time.
### Verification, delivery and limits
Post-hoc validation used benchmark commit `f106832febe525afe740a3d4504b57d51d75189b` and protocol `diskcover-minpoly-v1`. The opening version was not recorded; this cannot be described as a pre-frozen contract. Publisher tools were actually executed:
| Check | Result and limit |
|---|---|
| tools/check_tools.py | 39 synthetic checks passed, exit 0; not mathematical problem solving |
| tools/diskcover_answer.py | matches_reference: true, exit 0; integers were not converted through floating point |
| n=12 reference fingerprint | Exact match |
| Original mathematical deliverables | Complete proof, code, inputs, certificates and logs submitted |
| Original solve and later audit copy | Three-stage replays passed; self-review of the same model's work |
| Independent external mathematical review | Not performed |
| This report stage | Public tools and rounding checks rerun; geometry verifier not rerun |
The public fingerprint is `35d604a5ea1b1fe5c52c30337743c1a8142b69827023284f9597e1ca9cb8f947`. Matching compares encoded answer data only; it does not prove minimality, irreducibility, continuous coverage, global optimality, timing authenticity or resource-rule compliance.
Prior proof checks included modular irreducibility, Sturm isolation, a unique root box, full-disk coverage via triangular faces and circular caps, and global topology classification with Farkas and energy-tree exclusions. The earlier statement that floating point was used only for display was too absolute: the summary layer also compares floating-point report values. Acceptance relies separately on rational, outward-interval and symbolic checks. Self-review did not replace those checks with floating-point summaries and is not external certification.
The problem page displays **477 points**. Scoring is explained on the [problem page](n12.html) and [testing guide](guide.html), rather than repeated here. The publisher has settled the resource-rule interpretation; this remains a single retrospective record, with public submissions closed and no frozen formal comparison contract.
**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 later report, archival and website publication use local reports and the user-selected skill under separate explicit authorization. They do not retroactively establish compliance of the original solve.
### Downloadable records
[Machine-readable record](record-n12-astra-20261001.json) · [Report Markdown](record-n12-astra-20261001.en.md) · [Actual original input](reports/n12-astra-main-prompt.original.txt)
[Download this record's structured JSON](record-n12-astra-20261001.json). This public version contains input, resources, relative chronology, sources, check summaries and acceptance limits, but no mathematical answers, proof bundles, private paths, billing data or full chats.