{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:SMOUVT74XN64RAEJTF4DWZQCIX","short_pith_number":"pith:SMOUVT74","schema_version":"1.0","canonical_sha256":"931d4acffcbb7dc8808999783b660245c3fa131483f22f4087f0f91a64699fc1","source":{"kind":"arxiv","id":"2407.09264","version":3},"attestation_state":"computed","paper":{"title":"Computer-assisted methods in Sigma-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GR","authors_text":"Elisa Hartmann","submitted_at":"2024-07-12T13:47:38Z","abstract_excerpt":"We develop an algorithm for recognizing whether a character belongs to $\\Sigma^m$. In order to apply it we just need to know that the ambient group is of type $\\mathrm{FP}_m$ or of type $\\mathrm{F}_2$ and that the word problem is solvable for this group. Then finite data is sufficient proof of membership in $\\Sigma^m$, not just for the given character but also for a neighborhood of it."},"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":"2407.09264","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-07-12T13:47:38Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"36ac39b4215648c13056dc2d166990c998485129fef29b7fb15e95805065d441","abstract_canon_sha256":"f7e5cd1ef56746f36afda41a090469e34ee16d015e7d25fff189716ed09e65a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:10:32.054280Z","signature_b64":"h1syaiTZ9oN6K1pujUdp4S28GXp+ve5TioVBBT4OnG5vQee0YETG8mHYbIDl+7lpXtWxQDL4GE6f1D+OIuZdDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"931d4acffcbb7dc8808999783b660245c3fa131483f22f4087f0f91a64699fc1","last_reissued_at":"2026-07-05T09:10:32.053799Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:10:32.053799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computer-assisted methods in Sigma-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GR","authors_text":"Elisa Hartmann","submitted_at":"2024-07-12T13:47:38Z","abstract_excerpt":"We develop an algorithm for recognizing whether a character belongs to $\\Sigma^m$. In order to apply it we just need to know that the ambient group is of type $\\mathrm{FP}_m$ or of type $\\mathrm{F}_2$ and that the word problem is solvable for this group. Then finite data is sufficient proof of membership in $\\Sigma^m$, not just for the given character but also for a neighborhood of it."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.09264","kind":"arxiv","version":3},"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/2407.09264/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":"2407.09264","created_at":"2026-07-05T09:10:32.053859+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.09264v3","created_at":"2026-07-05T09:10:32.053859+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.09264","created_at":"2026-07-05T09:10:32.053859+00:00"},{"alias_kind":"pith_short_12","alias_value":"SMOUVT74XN64","created_at":"2026-07-05T09:10:32.053859+00:00"},{"alias_kind":"pith_short_16","alias_value":"SMOUVT74XN64RAEJ","created_at":"2026-07-05T09:10:32.053859+00:00"},{"alias_kind":"pith_short_8","alias_value":"SMOUVT74","created_at":"2026-07-05T09:10:32.053859+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.13272","citing_title":"Geometric invariants of locally compact groups: the homological perspective","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SMOUVT74XN64RAEJTF4DWZQCIX","json":"https://pith.science/pith/SMOUVT74XN64RAEJTF4DWZQCIX.json","graph_json":"https://pith.science/api/pith-number/SMOUVT74XN64RAEJTF4DWZQCIX/graph.json","events_json":"https://pith.science/api/pith-number/SMOUVT74XN64RAEJTF4DWZQCIX/events.json","paper":"https://pith.science/paper/SMOUVT74"},"agent_actions":{"view_html":"https://pith.science/pith/SMOUVT74XN64RAEJTF4DWZQCIX","download_json":"https://pith.science/pith/SMOUVT74XN64RAEJTF4DWZQCIX.json","view_paper":"https://pith.science/paper/SMOUVT74","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.09264&json=true","fetch_graph":"https://pith.science/api/pith-number/SMOUVT74XN64RAEJTF4DWZQCIX/graph.json","fetch_events":"https://pith.science/api/pith-number/SMOUVT74XN64RAEJTF4DWZQCIX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SMOUVT74XN64RAEJTF4DWZQCIX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SMOUVT74XN64RAEJTF4DWZQCIX/action/storage_attestation","attest_author":"https://pith.science/pith/SMOUVT74XN64RAEJTF4DWZQCIX/action/author_attestation","sign_citation":"https://pith.science/pith/SMOUVT74XN64RAEJTF4DWZQCIX/action/citation_signature","submit_replication":"https://pith.science/pith/SMOUVT74XN64RAEJTF4DWZQCIX/action/replication_record"}},"created_at":"2026-07-05T09:10:32.053859+00:00","updated_at":"2026-07-05T09:10:32.053859+00:00"}