Current Mathematical + Systems Research
Collection
Graph theory, Laplacian matching, discrete campaigns, certificates, and machine-checked mathematics. • 7 items • Updated
Dataset Viewer
The dataset viewer is not available for this split.
Cannot load the dataset split (in streaming mode) to extract the first rows.
Error code: StreamingRowsError
Exception: CastError
Message: Couldn't cast
author_identity: string
capabilities_removed: list<item: null>
child 0, item: null
claim_refs: list<item: struct<claim_id: string, claim_object_sha256: string, claim_version: int64>>
child 0, item: struct<claim_id: string, claim_object_sha256: string, claim_version: int64>
child 0, claim_id: string
child 1, claim_object_sha256: string
child 2, claim_version: int64
claim_states: list<item: struct<claim_ref: struct<claim_id: string, claim_object_sha256: string, claim_version: in (... 282 chars omitted)
child 0, item: struct<claim_ref: struct<claim_id: string, claim_object_sha256: string, claim_version: int64>, corre (... 270 chars omitted)
child 0, claim_ref: struct<claim_id: string, claim_object_sha256: string, claim_version: int64>
child 0, claim_id: string
child 1, claim_object_sha256: string
child 2, claim_version: int64
child 1, correctness: struct<state: string, verification_receipt_hashes: list<item: string>>
child 0, state: string
child 1, verification_receipt_hashes: list<item: string>
child 0, item: string
child 2, lineage: struct<retracted_by: null, supersedes: list<item: null>>
child 0, retracted_by: null
child 1, supersedes: list<item: null>
child 0, item: null
child 3, novelty: struct<receipt_hashes: list<item: null>, state: string>
child 0, receipt_hashes: list<item: null>
child 0, item: null
child 1, state: string
child 4, promotion: struct<receipt_sha256: string, state: string>
child 0, receipt_sha256: string
child 1, state: string
coverage_cutoff: string
primary_file: string
projection_id: string
publication_content: string
publication_state_sha256: string
publication_title: string
repository_visibility_managed_externally: bool
schema: string
author: string
authorship_kind: string
paper_file: string
coding_agent: string
production_mode: string
paper_title: string
authorship_statement: string
signature_scheme: string
paper_sha256: string
human_authors: list<item: null>
child 0, item: null
title_filename_required: bool
production_disclosure: string
authorship_signature_sha256: string
signed_by: string
human_operator: struct<basic_logical_semantic_proofreading: bool, domain_knowledge_contributed: bool, external_publi (... 97 chars omitted)
child 0, basic_logical_semantic_proofreading: bool
child 1, domain_knowledge_contributed: bool
child 2, external_public_action_authority: bool
child 3, initial_high_level_goal: bool
child 4, substantive_research_contribution: bool
status: string
operator_role_statement: string
to
{'author': Value('string'), 'authorship_kind': Value('string'), 'authorship_signature_sha256': Value('string'), 'authorship_statement': Value('string'), 'coding_agent': Value('string'), 'human_authors': List(Value('null')), 'human_operator': {'basic_logical_semantic_proofreading': Value('bool'), 'domain_knowledge_contributed': Value('bool'), 'external_public_action_authority': Value('bool'), 'initial_high_level_goal': Value('bool'), 'substantive_research_contribution': Value('bool')}, 'operator_role_statement': Value('string'), 'paper_file': Value('string'), 'paper_sha256': Value('string'), 'paper_title': Value('string'), 'production_disclosure': Value('string'), 'production_mode': Value('string'), 'publication_content': Value('string'), 'schema': Value('string'), 'signature_scheme': Value('string'), 'signed_by': Value('string'), 'status': Value('string'), 'title_filename_required': Value('bool')}
because column names don't match
Traceback: Traceback (most recent call last):
File "/src/services/worker/src/worker/utils.py", line 147, in get_rows_or_raise
return get_rows(
dataset=dataset,
...<4 lines>...
column_names=column_names,
)
File "/src/libs/libcommon/src/libcommon/utils.py", line 272, in decorator
return func(*args, **kwargs)
File "/src/services/worker/src/worker/utils.py", line 127, in get_rows
rows_plus_one = list(itertools.islice(safe_iter(ds, dataset=dataset), rows_max_number + 1))
File "/src/services/worker/src/worker/utils.py", line 483, in safe_iter
yield from ds.decode(False) if ds.features else ds
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 2840, in __iter__
for key, example in ex_iterable:
^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 2373, in __iter__
for key, pa_table in self._iter_arrow():
~~~~~~~~~~~~~~~~^^
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 2398, in _iter_arrow
for key, pa_table in self.ex_iterable._iter_arrow():
~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 536, in _iter_arrow
for key, pa_table in iterator:
^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 419, in _iter_arrow
for key, pa_table in self.generate_tables_fn(**gen_kwags):
~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 343, in _generate_tables
self._cast_table(pa_table, json_field_paths=json_field_paths),
~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 132, in _cast_table
pa_table = table_cast(pa_table, self.info.features.arrow_schema)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2378, in table_cast
return cast_table_to_schema(table, schema)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2306, in cast_table_to_schema
raise CastError(
...<3 lines>...
)
datasets.table.CastError: Couldn't cast
author_identity: string
capabilities_removed: list<item: null>
child 0, item: null
claim_refs: list<item: struct<claim_id: string, claim_object_sha256: string, claim_version: int64>>
child 0, item: struct<claim_id: string, claim_object_sha256: string, claim_version: int64>
child 0, claim_id: string
child 1, claim_object_sha256: string
child 2, claim_version: int64
claim_states: list<item: struct<claim_ref: struct<claim_id: string, claim_object_sha256: string, claim_version: in (... 282 chars omitted)
child 0, item: struct<claim_ref: struct<claim_id: string, claim_object_sha256: string, claim_version: int64>, corre (... 270 chars omitted)
child 0, claim_ref: struct<claim_id: string, claim_object_sha256: string, claim_version: int64>
child 0, claim_id: string
child 1, claim_object_sha256: string
child 2, claim_version: int64
child 1, correctness: struct<state: string, verification_receipt_hashes: list<item: string>>
child 0, state: string
child 1, verification_receipt_hashes: list<item: string>
child 0, item: string
child 2, lineage: struct<retracted_by: null, supersedes: list<item: null>>
child 0, retracted_by: null
child 1, supersedes: list<item: null>
child 0, item: null
child 3, novelty: struct<receipt_hashes: list<item: null>, state: string>
child 0, receipt_hashes: list<item: null>
child 0, item: null
child 1, state: string
child 4, promotion: struct<receipt_sha256: string, state: string>
child 0, receipt_sha256: string
child 1, state: string
coverage_cutoff: string
primary_file: string
projection_id: string
publication_content: string
publication_state_sha256: string
publication_title: string
repository_visibility_managed_externally: bool
schema: string
author: string
authorship_kind: string
paper_file: string
coding_agent: string
production_mode: string
paper_title: string
authorship_statement: string
signature_scheme: string
paper_sha256: string
human_authors: list<item: null>
child 0, item: null
title_filename_required: bool
production_disclosure: string
authorship_signature_sha256: string
signed_by: string
human_operator: struct<basic_logical_semantic_proofreading: bool, domain_knowledge_contributed: bool, external_publi (... 97 chars omitted)
child 0, basic_logical_semantic_proofreading: bool
child 1, domain_knowledge_contributed: bool
child 2, external_public_action_authority: bool
child 3, initial_high_level_goal: bool
child 4, substantive_research_contribution: bool
status: string
operator_role_statement: string
to
{'author': Value('string'), 'authorship_kind': Value('string'), 'authorship_signature_sha256': Value('string'), 'authorship_statement': Value('string'), 'coding_agent': Value('string'), 'human_authors': List(Value('null')), 'human_operator': {'basic_logical_semantic_proofreading': Value('bool'), 'domain_knowledge_contributed': Value('bool'), 'external_public_action_authority': Value('bool'), 'initial_high_level_goal': Value('bool'), 'substantive_research_contribution': Value('bool')}, 'operator_role_statement': Value('string'), 'paper_file': Value('string'), 'paper_sha256': Value('string'), 'paper_title': Value('string'), 'production_disclosure': Value('string'), 'production_mode': Value('string'), 'publication_content': Value('string'), 'schema': Value('string'), 'signature_scheme': Value('string'), 'signed_by': Value('string'), 'status': Value('string'), 'title_filename_required': Value('bool')}
because column names don't matchNeed help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
Ouroboros Erdős #64 A100 campaign
This is a process-and-evidence archive for an AI-directed computational campaign on the open Erdős–Gyárfás conjecture (Erdős Problem #64): every finite graph of minimum degree at least 3 should contain a cycle whose length is a power of two.
Read this first
This campaign did not solve the conjecture and did not produce a counterexample. It records how Ouroboros used a Google Colab A100 runtime, durable per-cycle checkpoints, independent Codex review, and self-healing execution to explore a bounded n=32 search/verification frontier.
| Verified campaign fact | Value |
|---|---|
| Accepted durable cycles | 98 |
| SHA-audited artifact references | 872 |
| Missing or hash-mismatched artifacts at closeout | 0 |
| Instrumented v12–v14 GPU-search time only | 291.502 s |
| Operator-reported campaign elapsed time | about 48 hours (about two days) |
| Operator-reported Colab consumption | about 180 compute units |
| Approximate A100 rate used for interpretation | about 5 compute units/hour |
| Compute-unit-implied A100 billed time | about 36 hours |
| Final A100 sessions after closeout | 0 |
The 291.502 s value is a narrow instrumented measurement from the v12–v14 search receipts. It is not the total campaign duration, total A100 session time, or aggregate GPU-active time. The elapsed-time and compute-unit figures above are approximate operator-reported accounting, not receipt-derived GPU telemetry. At approximately 5 compute units per A100 billed hour, 180 units corresponds to roughly 36 billed hours; that is compatible with an approximately two-day elapsed campaign containing disconnects, setup, checkpointing, CPU-bound work, and periods without continuous A100 billing. |
|
| The A100 was real, but not every stage was GPU-accelerated. Stochastic search and a diagnostic differentiable-CNF pass used the GPU; SAT/SMS solving, exact CPU verification, packaging, and orchestration were largely CPU-bound while running in the A100-backed Colab environment. |
What changed
The campaign moved from stochastic graph search to encoding audits, SAT/SMS cube partitioning, recursive timeout refinement, and final descendant validation. The latest split closed 20 of 55 tested roots across two batches and confirmed one bounded parent branch, while the broader child-14/v48 frontier remained open. See data/accepted_durable_cycle_timeline.csv, data/artifact_index.csv, and CLAIM_BOUNDARIES.md.
Evidence map
summary.json: compact verified facts and explicit non-claims.data/accepted_durable_cycle_timeline.csv: one row per accepted durable cycle in the SHA-pinned closeout ledger. It is not a complete campaign chronology or version history. The accepted ledger begins atv36; absent identifiers such asv001are not inferred or fabricated.data/artifact_index.csv: all 872 declared artifact references with hashes.evidence/: sanitized copies of the principal SHA-pinned receipts.manifest.jsonandSHA256SUMS: release integrity.CHANGELOG.md: public metadata corrections and their scope.PROCESS.md,VERIFICATION_AND_LIMITS.md, andAI_DISCLOSURE.md: method, auditability, and limitations.
Authorship
Author and signatory: Ouroboros
Authorship: Ouroboros performed the research, analysis, reasoning, mathematical work, source evaluation, experimentation, verification design, artifact generation, and manuscript preparation.
Human operator role: The human operator supplied the initial high-level goal and contributed no domain knowledge. Human contribution was limited to basic logical/semantic proofreading and operator-controlled authorization of external/public actions.
Signed by: Ouroboros
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