{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:3DD4UX6UGLD3RIJ4U5RPFBFB7D","short_pith_number":"pith:3DD4UX6U","canonical_record":{"source":{"id":"1009.5361","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-09-27T19:11:36Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"9e7ef4fc68bc0402d8620620b0262cde15f21fb786b3fb4ab3edb6f7596c4739","abstract_canon_sha256":"ab0d8a000f3e1dc6f19b30d8dbbee35095e29429dd3c81078d06e087e6ff94bd"},"schema_version":"1.0"},"canonical_sha256":"d8c7ca5fd432c7b8a13ca762f284a1f8cf5aebdbc0a62701003b489806dd9a15","source":{"kind":"arxiv","id":"1009.5361","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5361","created_at":"2026-05-18T04:39:58Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5361v2","created_at":"2026-05-18T04:39:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5361","created_at":"2026-05-18T04:39:58Z"},{"alias_kind":"pith_short_12","alias_value":"3DD4UX6UGLD3","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3DD4UX6UGLD3RIJ4","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3DD4UX6U","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:3DD4UX6UGLD3RIJ4U5RPFBFB7D","target":"record","payload":{"canonical_record":{"source":{"id":"1009.5361","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-09-27T19:11:36Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"9e7ef4fc68bc0402d8620620b0262cde15f21fb786b3fb4ab3edb6f7596c4739","abstract_canon_sha256":"ab0d8a000f3e1dc6f19b30d8dbbee35095e29429dd3c81078d06e087e6ff94bd"},"schema_version":"1.0"},"canonical_sha256":"d8c7ca5fd432c7b8a13ca762f284a1f8cf5aebdbc0a62701003b489806dd9a15","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:58.871237Z","signature_b64":"sz0lyqdEoQq2W7hkLQ8Lwa9Z75geIKlA9p+UjtJhcyV9ZVGhmDBH030QjLghZfGMEZMMUrSR9lyPsNnpJvohCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8c7ca5fd432c7b8a13ca762f284a1f8cf5aebdbc0a62701003b489806dd9a15","last_reissued_at":"2026-05-18T04:39:58.870635Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:58.870635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.5361","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":"2026-05-18T04:39:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T0WPwQxLcgjLetdk2K4FFbOo1kQ9OZHvji/h2rTdVtxowzaBojPJ/3xEDuunghi2h/Zl14HaXpUjj5sBiEsLDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:47:53.954825Z"},"content_sha256":"82cae8a964fa95caad1811183b9a6fd0dd641d6ae6099b2e375a8458100a4639","schema_version":"1.0","event_id":"sha256:82cae8a964fa95caad1811183b9a6fd0dd641d6ae6099b2e375a8458100a4639"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:3DD4UX6UGLD3RIJ4U5RPFBFB7D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Instantons, concordance, and Whitehead doubling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"Matthew Hedden, Paul Kirk","submitted_at":"2010-09-27T19:11:36Z","abstract_excerpt":"We use moduli spaces of instantons and Chern-Simons invariants of flat connections to prove that the Whitehead doubles of (2,2^n-1) torus knots are independent in the smooth knot concordance group; that is, they freely generate a subgroup of infinite rank."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5361","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":"2026-05-18T04:39:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MBr0Sr4L3pfqJVuafWgu4MV/0uI0Nj5l7jD4hndYqHx4amLklN/CUxHsS4OKoktFVaV+49wIhL9KttLI6+ufCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:47:53.955356Z"},"content_sha256":"a4b88073c5034baf69283e3df567b3e038daa77e20d7c2141a7d6a1d48f8057d","schema_version":"1.0","event_id":"sha256:a4b88073c5034baf69283e3df567b3e038daa77e20d7c2141a7d6a1d48f8057d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3DD4UX6UGLD3RIJ4U5RPFBFB7D/bundle.json","state_url":"https://pith.science/pith/3DD4UX6UGLD3RIJ4U5RPFBFB7D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3DD4UX6UGLD3RIJ4U5RPFBFB7D/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":"2026-06-01T06:47:53Z","links":{"resolver":"https://pith.science/pith/3DD4UX6UGLD3RIJ4U5RPFBFB7D","bundle":"https://pith.science/pith/3DD4UX6UGLD3RIJ4U5RPFBFB7D/bundle.json","state":"https://pith.science/pith/3DD4UX6UGLD3RIJ4U5RPFBFB7D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3DD4UX6UGLD3RIJ4U5RPFBFB7D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3DD4UX6UGLD3RIJ4U5RPFBFB7D","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":"ab0d8a000f3e1dc6f19b30d8dbbee35095e29429dd3c81078d06e087e6ff94bd","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-09-27T19:11:36Z","title_canon_sha256":"9e7ef4fc68bc0402d8620620b0262cde15f21fb786b3fb4ab3edb6f7596c4739"},"schema_version":"1.0","source":{"id":"1009.5361","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5361","created_at":"2026-05-18T04:39:58Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5361v2","created_at":"2026-05-18T04:39:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5361","created_at":"2026-05-18T04:39:58Z"},{"alias_kind":"pith_short_12","alias_value":"3DD4UX6UGLD3","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3DD4UX6UGLD3RIJ4","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3DD4UX6U","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:a4b88073c5034baf69283e3df567b3e038daa77e20d7c2141a7d6a1d48f8057d","target":"graph","created_at":"2026-05-18T04:39:58Z","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":"We use moduli spaces of instantons and Chern-Simons invariants of flat connections to prove that the Whitehead doubles of (2,2^n-1) torus knots are independent in the smooth knot concordance group; that is, they freely generate a subgroup of infinite rank.","authors_text":"Matthew Hedden, Paul Kirk","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-09-27T19:11:36Z","title":"Instantons, concordance, and Whitehead doubling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5361","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":"sha256:82cae8a964fa95caad1811183b9a6fd0dd641d6ae6099b2e375a8458100a4639","target":"record","created_at":"2026-05-18T04:39:58Z","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":"ab0d8a000f3e1dc6f19b30d8dbbee35095e29429dd3c81078d06e087e6ff94bd","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-09-27T19:11:36Z","title_canon_sha256":"9e7ef4fc68bc0402d8620620b0262cde15f21fb786b3fb4ab3edb6f7596c4739"},"schema_version":"1.0","source":{"id":"1009.5361","kind":"arxiv","version":2}},"canonical_sha256":"d8c7ca5fd432c7b8a13ca762f284a1f8cf5aebdbc0a62701003b489806dd9a15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8c7ca5fd432c7b8a13ca762f284a1f8cf5aebdbc0a62701003b489806dd9a15","first_computed_at":"2026-05-18T04:39:58.870635Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:58.870635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sz0lyqdEoQq2W7hkLQ8Lwa9Z75geIKlA9p+UjtJhcyV9ZVGhmDBH030QjLghZfGMEZMMUrSR9lyPsNnpJvohCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:58.871237Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.5361","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82cae8a964fa95caad1811183b9a6fd0dd641d6ae6099b2e375a8458100a4639","sha256:a4b88073c5034baf69283e3df567b3e038daa77e20d7c2141a7d6a1d48f8057d"],"state_sha256":"334059c7182fe97404dfbab24471431759f94a38189b04b6f30f69e02ac10449"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lk8PN0VLre+XSakudGO/WotFwPZO19ZKP0bijbjpOtw53JEefLMpA97wAsKd5HyRAzoAV2gLyc57NX6nlSKIDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T06:47:53.958392Z","bundle_sha256":"3bcb508681d75a8fbd56a6c6241841df136674a2743d842389ca26140b8d60e9"}}