{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:3BMPNM227AJIHU4IN6BSAORT7R","short_pith_number":"pith:3BMPNM22","canonical_record":{"source":{"id":"math/0701460","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2007-01-16T21:28:35Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"ed39c7f0c506f8b297128db48d33804172433432246bbf92af82cbed3d9208ec","abstract_canon_sha256":"2bc735447ebb690e3be4c5810acec09b7365b115727cc647b6a23a22d4d8d7e6"},"schema_version":"1.0"},"canonical_sha256":"d858f6b35af81283d3886f83203a33fc774d06594f415a00a9ca7b62adc49d03","source":{"kind":"arxiv","id":"math/0701460","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0701460","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"arxiv_version","alias_value":"math/0701460v2","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701460","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"pith_short_12","alias_value":"3BMPNM227AJI","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"3BMPNM227AJIHU4I","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"3BMPNM22","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:3BMPNM227AJIHU4IN6BSAORT7R","target":"record","payload":{"canonical_record":{"source":{"id":"math/0701460","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2007-01-16T21:28:35Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"ed39c7f0c506f8b297128db48d33804172433432246bbf92af82cbed3d9208ec","abstract_canon_sha256":"2bc735447ebb690e3be4c5810acec09b7365b115727cc647b6a23a22d4d8d7e6"},"schema_version":"1.0"},"canonical_sha256":"d858f6b35af81283d3886f83203a33fc774d06594f415a00a9ca7b62adc49d03","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:59.412117Z","signature_b64":"HBHF8sE4OcO22OONGyARkaiozvEkZ2HtWplLubLoX508Yd/h1ynnpls7cJoAR0ZhCKz6qABkID7uCwd0HYJJBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d858f6b35af81283d3886f83203a33fc774d06594f415a00a9ca7b62adc49d03","last_reissued_at":"2026-05-18T02:37:59.411737Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:59.411737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0701460","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":"2026-05-18T02:37:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dAYpYcpathLa5nwt3vxTGXvmggZFRb4yS7NNWSpRVGrPlWDZgJM1oHef8NcX/HyE+CqhpjYiIl0fUmpiNYTxCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:10:30.151412Z"},"content_sha256":"be0e9d7717bbba3adcfbdc3bbdc1c5338ab20a664e0ceed4bcfc2bd41866a80b","schema_version":"1.0","event_id":"sha256:be0e9d7717bbba3adcfbdc3bbdc1c5338ab20a664e0ceed4bcfc2bd41866a80b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:3BMPNM227AJIHU4IN6BSAORT7R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Knot concordance and Heegaard Floer homology invariants in branched covers","license":"","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Daniel Ruberman, J. Elisenda Grigsby, Saso Strle","submitted_at":"2007-01-16T21:28:35Z","abstract_excerpt":"By studying the Heegaard Floer homology of the preimage of a knot K in S^3 inside its double branched cover, we develop simple obstructions to K having finite order in the classical smooth concordance group. As an application, we prove that all 2-bridge knots of crossing number at most 12 for which the smooth concordance order was previously unknown have infinite smooth concordance order."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701460","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":"2026-05-18T02:37:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HrBOQqTJs83fuAERTu3/nKmOxNtqYhiHc0fol5c2DzIu7E+TbZfWCwUfs8Z5D7arwk6GNCJ0HvYhfMRIlFO/Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:10:30.152059Z"},"content_sha256":"c90b386a21667da16cc7e6484bb6669dbad6773f994babc81a8e3ed888cf938e","schema_version":"1.0","event_id":"sha256:c90b386a21667da16cc7e6484bb6669dbad6773f994babc81a8e3ed888cf938e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3BMPNM227AJIHU4IN6BSAORT7R/bundle.json","state_url":"https://pith.science/pith/3BMPNM227AJIHU4IN6BSAORT7R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3BMPNM227AJIHU4IN6BSAORT7R/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":"2026-05-27T06:10:30Z","links":{"resolver":"https://pith.science/pith/3BMPNM227AJIHU4IN6BSAORT7R","bundle":"https://pith.science/pith/3BMPNM227AJIHU4IN6BSAORT7R/bundle.json","state":"https://pith.science/pith/3BMPNM227AJIHU4IN6BSAORT7R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3BMPNM227AJIHU4IN6BSAORT7R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:3BMPNM227AJIHU4IN6BSAORT7R","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":"2bc735447ebb690e3be4c5810acec09b7365b115727cc647b6a23a22d4d8d7e6","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.GT","submitted_at":"2007-01-16T21:28:35Z","title_canon_sha256":"ed39c7f0c506f8b297128db48d33804172433432246bbf92af82cbed3d9208ec"},"schema_version":"1.0","source":{"id":"math/0701460","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0701460","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"arxiv_version","alias_value":"math/0701460v2","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701460","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"pith_short_12","alias_value":"3BMPNM227AJI","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"3BMPNM227AJIHU4I","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"3BMPNM22","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:c90b386a21667da16cc7e6484bb6669dbad6773f994babc81a8e3ed888cf938e","target":"graph","created_at":"2026-05-18T02:37:59Z","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":"By studying the Heegaard Floer homology of the preimage of a knot K in S^3 inside its double branched cover, we develop simple obstructions to K having finite order in the classical smooth concordance group. As an application, we prove that all 2-bridge knots of crossing number at most 12 for which the smooth concordance order was previously unknown have infinite smooth concordance order.","authors_text":"Daniel Ruberman, J. Elisenda Grigsby, Saso Strle","cross_cats":["math.SG"],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2007-01-16T21:28:35Z","title":"Knot concordance and Heegaard Floer homology invariants in branched covers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701460","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:be0e9d7717bbba3adcfbdc3bbdc1c5338ab20a664e0ceed4bcfc2bd41866a80b","target":"record","created_at":"2026-05-18T02:37:59Z","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":"2bc735447ebb690e3be4c5810acec09b7365b115727cc647b6a23a22d4d8d7e6","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.GT","submitted_at":"2007-01-16T21:28:35Z","title_canon_sha256":"ed39c7f0c506f8b297128db48d33804172433432246bbf92af82cbed3d9208ec"},"schema_version":"1.0","source":{"id":"math/0701460","kind":"arxiv","version":2}},"canonical_sha256":"d858f6b35af81283d3886f83203a33fc774d06594f415a00a9ca7b62adc49d03","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d858f6b35af81283d3886f83203a33fc774d06594f415a00a9ca7b62adc49d03","first_computed_at":"2026-05-18T02:37:59.411737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:59.411737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HBHF8sE4OcO22OONGyARkaiozvEkZ2HtWplLubLoX508Yd/h1ynnpls7cJoAR0ZhCKz6qABkID7uCwd0HYJJBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:59.412117Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0701460","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be0e9d7717bbba3adcfbdc3bbdc1c5338ab20a664e0ceed4bcfc2bd41866a80b","sha256:c90b386a21667da16cc7e6484bb6669dbad6773f994babc81a8e3ed888cf938e"],"state_sha256":"724d494fd2e79a47096ea5d5d2728105a503d7aec8d3706f7adb918cabc91990"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EhRFlwpBqET4HNx22x7t1Pj/K4BJ6Xs8jUNQxFKzqLlz82CnODyPvvEyV1ikojMdVLRurf1w0luBq6WYpAYVBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T06:10:30.155659Z","bundle_sha256":"4790f3499d9c60b5dcef9e67c5f08a5a1f273b3b4a62cde560e0725aea45d711"}}