{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:OS7PHKCEFJOV45YVW5MZRE5M2A","short_pith_number":"pith:OS7PHKCE","schema_version":"1.0","canonical_sha256":"74bef3a8442a5d5e7715b7599893acd01c3eb07f47df38d474c0a72b46b5d71f","source":{"kind":"arxiv","id":"1207.1310","version":1},"attestation_state":"computed","paper":{"title":"Thick Spanier groups and the first shape group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Jeremy Brazas, Paul Fabel","submitted_at":"2012-07-05T17:52:46Z","abstract_excerpt":"We develop a new route through which to explore $\\ker\\Psi_X$, the kernel of the $\\pi_1$-shape group homomorphism determined by a general space $X$, and establish, for each locally path connected, paracompact Hausdorff space $X$, $\\ker\\Psi_X$ is precisely the Spanier group of $X$."},"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":"1207.1310","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-07-05T17:52:46Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"800c8ee352dca5a4bb0ddb760eacb158f3925dbbbef2f1affdd02f408d4f928c","abstract_canon_sha256":"46512112e3ebd6e3d7e417315db1065756f3ffae1eac83c403ad4885523c5829"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:55.541034Z","signature_b64":"+oiq4rwY/SJmyksKONmj/j50GeRL6eRPNMcF95+0EBXazO+OBM17eWUeyT28UxkgofGVcVBgrBCN0l2K/BCtAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74bef3a8442a5d5e7715b7599893acd01c3eb07f47df38d474c0a72b46b5d71f","last_reissued_at":"2026-05-18T00:48:55.540284Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:55.540284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Thick Spanier groups and the first shape group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Jeremy Brazas, Paul Fabel","submitted_at":"2012-07-05T17:52:46Z","abstract_excerpt":"We develop a new route through which to explore $\\ker\\Psi_X$, the kernel of the $\\pi_1$-shape group homomorphism determined by a general space $X$, and establish, for each locally path connected, paracompact Hausdorff space $X$, $\\ker\\Psi_X$ is precisely the Spanier group of $X$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1310","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":""},"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":"1207.1310","created_at":"2026-05-18T00:48:55.540421+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.1310v1","created_at":"2026-05-18T00:48:55.540421+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1310","created_at":"2026-05-18T00:48:55.540421+00:00"},{"alias_kind":"pith_short_12","alias_value":"OS7PHKCEFJOV","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"OS7PHKCEFJOV45YV","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"OS7PHKCE","created_at":"2026-05-18T12:27:16.716162+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OS7PHKCEFJOV45YVW5MZRE5M2A","json":"https://pith.science/pith/OS7PHKCEFJOV45YVW5MZRE5M2A.json","graph_json":"https://pith.science/api/pith-number/OS7PHKCEFJOV45YVW5MZRE5M2A/graph.json","events_json":"https://pith.science/api/pith-number/OS7PHKCEFJOV45YVW5MZRE5M2A/events.json","paper":"https://pith.science/paper/OS7PHKCE"},"agent_actions":{"view_html":"https://pith.science/pith/OS7PHKCEFJOV45YVW5MZRE5M2A","download_json":"https://pith.science/pith/OS7PHKCEFJOV45YVW5MZRE5M2A.json","view_paper":"https://pith.science/paper/OS7PHKCE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.1310&json=true","fetch_graph":"https://pith.science/api/pith-number/OS7PHKCEFJOV45YVW5MZRE5M2A/graph.json","fetch_events":"https://pith.science/api/pith-number/OS7PHKCEFJOV45YVW5MZRE5M2A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OS7PHKCEFJOV45YVW5MZRE5M2A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OS7PHKCEFJOV45YVW5MZRE5M2A/action/storage_attestation","attest_author":"https://pith.science/pith/OS7PHKCEFJOV45YVW5MZRE5M2A/action/author_attestation","sign_citation":"https://pith.science/pith/OS7PHKCEFJOV45YVW5MZRE5M2A/action/citation_signature","submit_replication":"https://pith.science/pith/OS7PHKCEFJOV45YVW5MZRE5M2A/action/replication_record"}},"created_at":"2026-05-18T00:48:55.540421+00:00","updated_at":"2026-05-18T00:48:55.540421+00:00"}