{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:YEJDSNEGXQW764UDG5BQTNNP5L","short_pith_number":"pith:YEJDSNEG","schema_version":"1.0","canonical_sha256":"c112393486bc2dff7283374309b5afeafd34d6aec17265ac265aca3d531a967e","source":{"kind":"arxiv","id":"2507.17780","version":1},"attestation_state":"computed","paper":{"title":"In Reverie Together: Ten Years of Mathematical Discovery with a Machine Collaborator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","math.CO"],"primary_cat":"cs.DM","authors_text":"Boris Brimkov, Randy Davila, Ryan Pepper","submitted_at":"2025-07-23T00:49:32Z","abstract_excerpt":"We present four open conjectures in graph theory generated by the automated conjecturing system \\texttt{TxGraffiti}. Each conjecture is concise, grounded in natural graph invariants, and empirically validated across hundreds of graphs. Despite extensive effort, these statements remain unresolved--defying both proof and counterexample. They are not only mathematical challenges but creative expressions--born of symbolic pattern recognition and mathematician-defined heuristics, refined through years of human dialogue, and now offered back to the community as collaborative artifacts. These conject"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2507.17780","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2025-07-23T00:49:32Z","cross_cats_sorted":["cs.AI","math.CO"],"title_canon_sha256":"c6b88ef15d61ecece5af8f1d10fa008a6cc692b3f589e88c1a0daba0faeac4bc","abstract_canon_sha256":"e414a0181b96de9c7acd86ef5b928251e58d7e8bad24c245a7f2d2538814f8b7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:42:35.056917Z","signature_b64":"oNI9y2JmiKFS4YERWt27rlSXNeT50x8m5rHq75mxZHTjQakJ/Lnpow9Nvx8wN7Z/gc71qlE3GP1kFJx+8HynCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c112393486bc2dff7283374309b5afeafd34d6aec17265ac265aca3d531a967e","last_reissued_at":"2026-07-05T11:42:35.056352Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:42:35.056352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"In Reverie Together: Ten Years of Mathematical Discovery with a Machine Collaborator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","math.CO"],"primary_cat":"cs.DM","authors_text":"Boris Brimkov, Randy Davila, Ryan Pepper","submitted_at":"2025-07-23T00:49:32Z","abstract_excerpt":"We present four open conjectures in graph theory generated by the automated conjecturing system \\texttt{TxGraffiti}. Each conjecture is concise, grounded in natural graph invariants, and empirically validated across hundreds of graphs. Despite extensive effort, these statements remain unresolved--defying both proof and counterexample. They are not only mathematical challenges but creative expressions--born of symbolic pattern recognition and mathematician-defined heuristics, refined through years of human dialogue, and now offered back to the community as collaborative artifacts. These conject"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.17780","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.17780/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2507.17780","created_at":"2026-07-05T11:42:35.056418+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.17780v1","created_at":"2026-07-05T11:42:35.056418+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.17780","created_at":"2026-07-05T11:42:35.056418+00:00"},{"alias_kind":"pith_short_12","alias_value":"YEJDSNEGXQW7","created_at":"2026-07-05T11:42:35.056418+00:00"},{"alias_kind":"pith_short_16","alias_value":"YEJDSNEGXQW764UD","created_at":"2026-07-05T11:42:35.056418+00:00"},{"alias_kind":"pith_short_8","alias_value":"YEJDSNEG","created_at":"2026-07-05T11:42:35.056418+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.15761","citing_title":"Sharp bounds between the saturation number and the harmonic index","ref_index":6,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YEJDSNEGXQW764UDG5BQTNNP5L","json":"https://pith.science/pith/YEJDSNEGXQW764UDG5BQTNNP5L.json","graph_json":"https://pith.science/api/pith-number/YEJDSNEGXQW764UDG5BQTNNP5L/graph.json","events_json":"https://pith.science/api/pith-number/YEJDSNEGXQW764UDG5BQTNNP5L/events.json","paper":"https://pith.science/paper/YEJDSNEG"},"agent_actions":{"view_html":"https://pith.science/pith/YEJDSNEGXQW764UDG5BQTNNP5L","download_json":"https://pith.science/pith/YEJDSNEGXQW764UDG5BQTNNP5L.json","view_paper":"https://pith.science/paper/YEJDSNEG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.17780&json=true","fetch_graph":"https://pith.science/api/pith-number/YEJDSNEGXQW764UDG5BQTNNP5L/graph.json","fetch_events":"https://pith.science/api/pith-number/YEJDSNEGXQW764UDG5BQTNNP5L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YEJDSNEGXQW764UDG5BQTNNP5L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YEJDSNEGXQW764UDG5BQTNNP5L/action/storage_attestation","attest_author":"https://pith.science/pith/YEJDSNEGXQW764UDG5BQTNNP5L/action/author_attestation","sign_citation":"https://pith.science/pith/YEJDSNEGXQW764UDG5BQTNNP5L/action/citation_signature","submit_replication":"https://pith.science/pith/YEJDSNEGXQW764UDG5BQTNNP5L/action/replication_record"}},"created_at":"2026-07-05T11:42:35.056418+00:00","updated_at":"2026-07-05T11:42:35.056418+00:00"}