{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:UN6Q73GHMLPIL6OND6TM323MW2","short_pith_number":"pith:UN6Q73GH","canonical_record":{"source":{"id":"0709.0416","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2007-09-04T12:48:30Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"00f4168dc9523f1c12b703fe1b3f90ea7c2eeda19bff94ee67228a514818a139","abstract_canon_sha256":"61a9f8094358934a0b68a941e2ada89de9651ac0a4f14c48b7cface703bd21bc"},"schema_version":"1.0"},"canonical_sha256":"a37d0fecc762de85f9cd1fa6cdeb6cb6abf2661ec5e02695eacd2ea787134cc8","source":{"kind":"arxiv","id":"0709.0416","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0709.0416","created_at":"2026-05-18T04:33:36Z"},{"alias_kind":"arxiv_version","alias_value":"0709.0416v1","created_at":"2026-05-18T04:33:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.0416","created_at":"2026-05-18T04:33:36Z"},{"alias_kind":"pith_short_12","alias_value":"UN6Q73GHMLPI","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"UN6Q73GHMLPIL6ON","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"UN6Q73GH","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:UN6Q73GHMLPIL6OND6TM323MW2","target":"record","payload":{"canonical_record":{"source":{"id":"0709.0416","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2007-09-04T12:48:30Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"00f4168dc9523f1c12b703fe1b3f90ea7c2eeda19bff94ee67228a514818a139","abstract_canon_sha256":"61a9f8094358934a0b68a941e2ada89de9651ac0a4f14c48b7cface703bd21bc"},"schema_version":"1.0"},"canonical_sha256":"a37d0fecc762de85f9cd1fa6cdeb6cb6abf2661ec5e02695eacd2ea787134cc8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:36.790231Z","signature_b64":"J8Kt2RRpYtUVDpEXHHFE/dgvuURSMnpDAUWq5I9zm/aRDkLWJfisHCLbDfvnzTH3ZznJOVPoXcDo0KL82Is+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a37d0fecc762de85f9cd1fa6cdeb6cb6abf2661ec5e02695eacd2ea787134cc8","last_reissued_at":"2026-05-18T04:33:36.789363Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:36.789363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0709.0416","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:33:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D6qeig85iOcBkW3VyMhF1xvNSS3h673FW6cjeiFAlaiEGxz3Kv7QwfrflKTSPRoEmfHfWWmXrZEnLaQUb4xgDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T02:59:14.939925Z"},"content_sha256":"5553a2245c6e0d893e17ed823b290e748eecda9b0432430f1adaa6aa85ee5426","schema_version":"1.0","event_id":"sha256:5553a2245c6e0d893e17ed823b290e748eecda9b0432430f1adaa6aa85ee5426"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:UN6Q73GHMLPIL6OND6TM323MW2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Freiheitss\\\"{a}tze for one-relator quotients of surface groups and of limit groups","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"James Howie, Muhammad Sarwar Saeed","submitted_at":"2007-09-04T12:48:30Z","abstract_excerpt":"Three versions of the Freiheitssatz are proved in the context of one-relator quotients of limit groups, where the latter are equipped with 1-acylindrical splittings over cyclic subgroups. These are natural extensions of previously published corresponding statements for one-relator quotients of orientable surface groups. Two of the proofs are new even in that restricted context."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.0416","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:33:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cXUrnOLOR4FGwXlngcbjk70U1Ph57JAkGZsZFxMeeUX/+1uYr4HNFv28S1Fs9et6rIB+gqBr7N6yctGI1nFGBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T02:59:14.940260Z"},"content_sha256":"d5a6286b962c69069d980180b55566a5b5c63adec78d368416b79a97667504df","schema_version":"1.0","event_id":"sha256:d5a6286b962c69069d980180b55566a5b5c63adec78d368416b79a97667504df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UN6Q73GHMLPIL6OND6TM323MW2/bundle.json","state_url":"https://pith.science/pith/UN6Q73GHMLPIL6OND6TM323MW2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UN6Q73GHMLPIL6OND6TM323MW2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T02:59:14Z","links":{"resolver":"https://pith.science/pith/UN6Q73GHMLPIL6OND6TM323MW2","bundle":"https://pith.science/pith/UN6Q73GHMLPIL6OND6TM323MW2/bundle.json","state":"https://pith.science/pith/UN6Q73GHMLPIL6OND6TM323MW2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UN6Q73GHMLPIL6OND6TM323MW2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:UN6Q73GHMLPIL6OND6TM323MW2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"61a9f8094358934a0b68a941e2ada89de9651ac0a4f14c48b7cface703bd21bc","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.GR","submitted_at":"2007-09-04T12:48:30Z","title_canon_sha256":"00f4168dc9523f1c12b703fe1b3f90ea7c2eeda19bff94ee67228a514818a139"},"schema_version":"1.0","source":{"id":"0709.0416","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0709.0416","created_at":"2026-05-18T04:33:36Z"},{"alias_kind":"arxiv_version","alias_value":"0709.0416v1","created_at":"2026-05-18T04:33:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.0416","created_at":"2026-05-18T04:33:36Z"},{"alias_kind":"pith_short_12","alias_value":"UN6Q73GHMLPI","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"UN6Q73GHMLPIL6ON","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"UN6Q73GH","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:d5a6286b962c69069d980180b55566a5b5c63adec78d368416b79a97667504df","target":"graph","created_at":"2026-05-18T04:33:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Three versions of the Freiheitssatz are proved in the context of one-relator quotients of limit groups, where the latter are equipped with 1-acylindrical splittings over cyclic subgroups. These are natural extensions of previously published corresponding statements for one-relator quotients of orientable surface groups. Two of the proofs are new even in that restricted context.","authors_text":"James Howie, Muhammad Sarwar Saeed","cross_cats":["math.GT"],"headline":"","license":"","primary_cat":"math.GR","submitted_at":"2007-09-04T12:48:30Z","title":"Freiheitss\\\"{a}tze for one-relator quotients of surface groups and of limit groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.0416","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5553a2245c6e0d893e17ed823b290e748eecda9b0432430f1adaa6aa85ee5426","target":"record","created_at":"2026-05-18T04:33:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"61a9f8094358934a0b68a941e2ada89de9651ac0a4f14c48b7cface703bd21bc","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.GR","submitted_at":"2007-09-04T12:48:30Z","title_canon_sha256":"00f4168dc9523f1c12b703fe1b3f90ea7c2eeda19bff94ee67228a514818a139"},"schema_version":"1.0","source":{"id":"0709.0416","kind":"arxiv","version":1}},"canonical_sha256":"a37d0fecc762de85f9cd1fa6cdeb6cb6abf2661ec5e02695eacd2ea787134cc8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a37d0fecc762de85f9cd1fa6cdeb6cb6abf2661ec5e02695eacd2ea787134cc8","first_computed_at":"2026-05-18T04:33:36.789363Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:36.789363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J8Kt2RRpYtUVDpEXHHFE/dgvuURSMnpDAUWq5I9zm/aRDkLWJfisHCLbDfvnzTH3ZznJOVPoXcDo0KL82Is+BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:36.790231Z","signed_message":"canonical_sha256_bytes"},"source_id":"0709.0416","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5553a2245c6e0d893e17ed823b290e748eecda9b0432430f1adaa6aa85ee5426","sha256:d5a6286b962c69069d980180b55566a5b5c63adec78d368416b79a97667504df"],"state_sha256":"ddc216c646665d5a04a0561e059c10ab9ce914152c4ae2e2a1d74f6abe6e0df0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JUxZEByY333nt1bHyNRNlQqcYDKiQ/hI4j0wt/ksI78M2DX+LPWw2diBOikU4TEHhdQh4a5eYqFLNJfQj1+bDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T02:59:14.942165Z","bundle_sha256":"c1966cc5aea289ac7c76eb4a618c81bbbb4a53e76aa6f00c72e0d48d8f09f1af"}}