{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:IL6XOUGRI2SBKAIXBHRR4ZE57A","short_pith_number":"pith:IL6XOUGR","canonical_record":{"source":{"id":"0907.4577","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-07-27T10:06:53Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"0402fbe5e61f4e6ac77bc6abcc13754860a7962c45eb9e982b2676fd0e63f85d","abstract_canon_sha256":"8e10a521c9f66464f0abb68a825ffe87842eb5de9541a7f624d63798887e0da7"},"schema_version":"1.0"},"canonical_sha256":"42fd7750d146a415011709e31e649df838c4c41c0df9e2edbf8bed8e9aebaecd","source":{"kind":"arxiv","id":"0907.4577","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.4577","created_at":"2026-05-18T03:32:28Z"},{"alias_kind":"arxiv_version","alias_value":"0907.4577v2","created_at":"2026-05-18T03:32:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.4577","created_at":"2026-05-18T03:32:28Z"},{"alias_kind":"pith_short_12","alias_value":"IL6XOUGRI2SB","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"IL6XOUGRI2SBKAIX","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"IL6XOUGR","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:IL6XOUGRI2SBKAIXBHRR4ZE57A","target":"record","payload":{"canonical_record":{"source":{"id":"0907.4577","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-07-27T10:06:53Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"0402fbe5e61f4e6ac77bc6abcc13754860a7962c45eb9e982b2676fd0e63f85d","abstract_canon_sha256":"8e10a521c9f66464f0abb68a825ffe87842eb5de9541a7f624d63798887e0da7"},"schema_version":"1.0"},"canonical_sha256":"42fd7750d146a415011709e31e649df838c4c41c0df9e2edbf8bed8e9aebaecd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:28.849851Z","signature_b64":"p8CREFGESp2zaRZ6Gc7FJj2MIS5x2ehGopRmLpc1Po4I9UxMWA23XXynEDSCbXcOzLT9lnRvAL0LuSNtT+nDAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42fd7750d146a415011709e31e649df838c4c41c0df9e2edbf8bed8e9aebaecd","last_reissued_at":"2026-05-18T03:32:28.849305Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:28.849305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0907.4577","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:32:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M8rQ6g6PYAfWc82sbBHs+AGTtmT/hn1JOjSDicHinY+HXpOx6HnX1xcUpvBHb8m9yXZG4OhppzHPdahApsivDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T03:38:50.727840Z"},"content_sha256":"4c202ad6ba359c3f247510182317e13997224074b6c4c2d957df9721f03902de","schema_version":"1.0","event_id":"sha256:4c202ad6ba359c3f247510182317e13997224074b6c4c2d957df9721f03902de"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:IL6XOUGRI2SBKAIXBHRR4ZE57A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asphericity and small cancellation theory for rotation family of groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"R\\'emi Coulon","submitted_at":"2009-07-27T10:06:53Z","abstract_excerpt":"Using small cancellation for rotating families of groups, we construct new examples of aspherical polyhedra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.4577","kind":"arxiv","version":2},"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":"2026-05-18T03:32:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v68w4smCcDPOthkdVngas5r/VrnH3fl4o/lu+cWD5jwsPQsFK6tfWN6D3LLEJmUkTQeoRDzo/7gmWhYeUTbtCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T03:38:50.728526Z"},"content_sha256":"6d55a23e44d0449ca7625e1464814cd4ee3f4b0f122c1746569cad04fbe3a10d","schema_version":"1.0","event_id":"sha256:6d55a23e44d0449ca7625e1464814cd4ee3f4b0f122c1746569cad04fbe3a10d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IL6XOUGRI2SBKAIXBHRR4ZE57A/bundle.json","state_url":"https://pith.science/pith/IL6XOUGRI2SBKAIXBHRR4ZE57A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IL6XOUGRI2SBKAIXBHRR4ZE57A/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":"2026-06-10T03:38:50Z","links":{"resolver":"https://pith.science/pith/IL6XOUGRI2SBKAIXBHRR4ZE57A","bundle":"https://pith.science/pith/IL6XOUGRI2SBKAIXBHRR4ZE57A/bundle.json","state":"https://pith.science/pith/IL6XOUGRI2SBKAIXBHRR4ZE57A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IL6XOUGRI2SBKAIXBHRR4ZE57A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:IL6XOUGRI2SBKAIXBHRR4ZE57A","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":"8e10a521c9f66464f0abb68a825ffe87842eb5de9541a7f624d63798887e0da7","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-07-27T10:06:53Z","title_canon_sha256":"0402fbe5e61f4e6ac77bc6abcc13754860a7962c45eb9e982b2676fd0e63f85d"},"schema_version":"1.0","source":{"id":"0907.4577","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.4577","created_at":"2026-05-18T03:32:28Z"},{"alias_kind":"arxiv_version","alias_value":"0907.4577v2","created_at":"2026-05-18T03:32:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.4577","created_at":"2026-05-18T03:32:28Z"},{"alias_kind":"pith_short_12","alias_value":"IL6XOUGRI2SB","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"IL6XOUGRI2SBKAIX","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"IL6XOUGR","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:6d55a23e44d0449ca7625e1464814cd4ee3f4b0f122c1746569cad04fbe3a10d","target":"graph","created_at":"2026-05-18T03:32:28Z","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":"Using small cancellation for rotating families of groups, we construct new examples of aspherical polyhedra.","authors_text":"R\\'emi Coulon","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-07-27T10:06:53Z","title":"Asphericity and small cancellation theory for rotation family of groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.4577","kind":"arxiv","version":2},"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":"sha256:4c202ad6ba359c3f247510182317e13997224074b6c4c2d957df9721f03902de","target":"record","created_at":"2026-05-18T03:32:28Z","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":"8e10a521c9f66464f0abb68a825ffe87842eb5de9541a7f624d63798887e0da7","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-07-27T10:06:53Z","title_canon_sha256":"0402fbe5e61f4e6ac77bc6abcc13754860a7962c45eb9e982b2676fd0e63f85d"},"schema_version":"1.0","source":{"id":"0907.4577","kind":"arxiv","version":2}},"canonical_sha256":"42fd7750d146a415011709e31e649df838c4c41c0df9e2edbf8bed8e9aebaecd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42fd7750d146a415011709e31e649df838c4c41c0df9e2edbf8bed8e9aebaecd","first_computed_at":"2026-05-18T03:32:28.849305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:28.849305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p8CREFGESp2zaRZ6Gc7FJj2MIS5x2ehGopRmLpc1Po4I9UxMWA23XXynEDSCbXcOzLT9lnRvAL0LuSNtT+nDAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:28.849851Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.4577","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c202ad6ba359c3f247510182317e13997224074b6c4c2d957df9721f03902de","sha256:6d55a23e44d0449ca7625e1464814cd4ee3f4b0f122c1746569cad04fbe3a10d"],"state_sha256":"f85fd0b6e1d87e8aed41cb912a2418f76822f7ea5d4d50f2d49a7dde17ec6f7f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eCQ6wc4foE5P3iNgPDbd+x+NQlXu0DiVjW70pBoZBbqYY9/rD0HeThXvaYrcwQ3FBX+ZOY8SAwDLlqs9qv8pDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T03:38:50.732750Z","bundle_sha256":"b4c003fd9bd47d99b0dc214bfa6a4a5f78a25abb8f24a4d1adb7fd795b7f80e0"}}