{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:J7XTBFHCSXDO7RBEREZFROLIUA","short_pith_number":"pith:J7XTBFHC","canonical_record":{"source":{"id":"0704.3669","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2007-04-27T07:12:16Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"6a1ee0d0aa9487e1f386481a922ca2e575a67dd0c9945a6b80a9879de7857054","abstract_canon_sha256":"c68071c1ffd670cf33f5aa3bd9077e58e0bfe1593fb8020cf8239eead9a17ac9"},"schema_version":"1.0"},"canonical_sha256":"4fef3094e295c6efc424893258b968a018aaa2019a6dde2ba5ceb43db4e94f89","source":{"kind":"arxiv","id":"0704.3669","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.3669","created_at":"2026-05-18T02:54:22Z"},{"alias_kind":"arxiv_version","alias_value":"0704.3669v1","created_at":"2026-05-18T02:54:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.3669","created_at":"2026-05-18T02:54:22Z"},{"alias_kind":"pith_short_12","alias_value":"J7XTBFHCSXDO","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"J7XTBFHCSXDO7RBE","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"J7XTBFHC","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:J7XTBFHCSXDO7RBEREZFROLIUA","target":"record","payload":{"canonical_record":{"source":{"id":"0704.3669","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2007-04-27T07:12:16Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"6a1ee0d0aa9487e1f386481a922ca2e575a67dd0c9945a6b80a9879de7857054","abstract_canon_sha256":"c68071c1ffd670cf33f5aa3bd9077e58e0bfe1593fb8020cf8239eead9a17ac9"},"schema_version":"1.0"},"canonical_sha256":"4fef3094e295c6efc424893258b968a018aaa2019a6dde2ba5ceb43db4e94f89","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:22.539046Z","signature_b64":"NUkDgG8z7nuuKVox6erUhv6hzrWM2INYDkiIbReOETs3sRbDELuKcG+InCCEeCAa4CccoXyNCXL9wQfXb7SnBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fef3094e295c6efc424893258b968a018aaa2019a6dde2ba5ceb43db4e94f89","last_reissued_at":"2026-05-18T02:54:22.538534Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:22.538534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0704.3669","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":"2026-05-18T02:54:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V/LH9+V5Z+QVtqnq7Djbs0ZoCHpA/dtlXmpBKzxvQthF7zCYGY7BHJZ9TSv4FMVOwMtQjoAWXSnVTK/INQcxBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T07:26:12.110015Z"},"content_sha256":"f59cdd294a4ba7e0363e37db81cf0755a9fb64b021fca703230a50fefd6dd682","schema_version":"1.0","event_id":"sha256:f59cdd294a4ba7e0363e37db81cf0755a9fb64b021fca703230a50fefd6dd682"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:J7XTBFHCSXDO7RBEREZFROLIUA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unified quantum invariants and their refinements for homology 3-spheres with 2-torsion","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.QA","authors_text":"Anna Beliakova, Christian Blanchet, Thang T. Q. Le","submitted_at":"2007-04-27T07:12:16Z","abstract_excerpt":"For every rational homology 3-sphere with 2-torsion only we construct a unified invariant (which takes values in a certain cyclotomic completion of a polynomial ring), such that the evaluation of this invariant at any odd root of unity provides the SO(3) Witten-Reshetikhin-Turaev invariant at this root and at any even root of unity the SU(2) quantum invariant. Moreover, this unified invariant splits into a sum of the refined unified invariants dominating spin and cohomological refinements of quantum SU(2) invariants. New results on the Ohtsuki series and the integrality of quantum invariants a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.3669","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":"2026-05-18T02:54:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vFZbwV/GPJjJxXM6AwSTfGubXinAMTYLnGIXO0/90dSQwrR1x5Ui0qBNa6fYtLVP7el9Z+uwuYga7FfOYWljCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T07:26:12.110783Z"},"content_sha256":"0d62d92e8b3ead500dfe6bbf442ef3b8b05ad9094bc3cce16ad7b1a5bb591cf4","schema_version":"1.0","event_id":"sha256:0d62d92e8b3ead500dfe6bbf442ef3b8b05ad9094bc3cce16ad7b1a5bb591cf4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J7XTBFHCSXDO7RBEREZFROLIUA/bundle.json","state_url":"https://pith.science/pith/J7XTBFHCSXDO7RBEREZFROLIUA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J7XTBFHCSXDO7RBEREZFROLIUA/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":"2026-05-25T07:26:12Z","links":{"resolver":"https://pith.science/pith/J7XTBFHCSXDO7RBEREZFROLIUA","bundle":"https://pith.science/pith/J7XTBFHCSXDO7RBEREZFROLIUA/bundle.json","state":"https://pith.science/pith/J7XTBFHCSXDO7RBEREZFROLIUA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J7XTBFHCSXDO7RBEREZFROLIUA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:J7XTBFHCSXDO7RBEREZFROLIUA","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":"c68071c1ffd670cf33f5aa3bd9077e58e0bfe1593fb8020cf8239eead9a17ac9","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.QA","submitted_at":"2007-04-27T07:12:16Z","title_canon_sha256":"6a1ee0d0aa9487e1f386481a922ca2e575a67dd0c9945a6b80a9879de7857054"},"schema_version":"1.0","source":{"id":"0704.3669","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0704.3669","created_at":"2026-05-18T02:54:22Z"},{"alias_kind":"arxiv_version","alias_value":"0704.3669v1","created_at":"2026-05-18T02:54:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.3669","created_at":"2026-05-18T02:54:22Z"},{"alias_kind":"pith_short_12","alias_value":"J7XTBFHCSXDO","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"J7XTBFHCSXDO7RBE","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"J7XTBFHC","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:0d62d92e8b3ead500dfe6bbf442ef3b8b05ad9094bc3cce16ad7b1a5bb591cf4","target":"graph","created_at":"2026-05-18T02:54:22Z","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":"For every rational homology 3-sphere with 2-torsion only we construct a unified invariant (which takes values in a certain cyclotomic completion of a polynomial ring), such that the evaluation of this invariant at any odd root of unity provides the SO(3) Witten-Reshetikhin-Turaev invariant at this root and at any even root of unity the SU(2) quantum invariant. Moreover, this unified invariant splits into a sum of the refined unified invariants dominating spin and cohomological refinements of quantum SU(2) invariants. New results on the Ohtsuki series and the integrality of quantum invariants a","authors_text":"Anna Beliakova, Christian Blanchet, Thang T. Q. Le","cross_cats":["math.GT"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2007-04-27T07:12:16Z","title":"Unified quantum invariants and their refinements for homology 3-spheres with 2-torsion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.3669","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:f59cdd294a4ba7e0363e37db81cf0755a9fb64b021fca703230a50fefd6dd682","target":"record","created_at":"2026-05-18T02:54:22Z","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":"c68071c1ffd670cf33f5aa3bd9077e58e0bfe1593fb8020cf8239eead9a17ac9","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.QA","submitted_at":"2007-04-27T07:12:16Z","title_canon_sha256":"6a1ee0d0aa9487e1f386481a922ca2e575a67dd0c9945a6b80a9879de7857054"},"schema_version":"1.0","source":{"id":"0704.3669","kind":"arxiv","version":1}},"canonical_sha256":"4fef3094e295c6efc424893258b968a018aaa2019a6dde2ba5ceb43db4e94f89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4fef3094e295c6efc424893258b968a018aaa2019a6dde2ba5ceb43db4e94f89","first_computed_at":"2026-05-18T02:54:22.538534Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:22.538534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NUkDgG8z7nuuKVox6erUhv6hzrWM2INYDkiIbReOETs3sRbDELuKcG+InCCEeCAa4CccoXyNCXL9wQfXb7SnBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:22.539046Z","signed_message":"canonical_sha256_bytes"},"source_id":"0704.3669","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f59cdd294a4ba7e0363e37db81cf0755a9fb64b021fca703230a50fefd6dd682","sha256:0d62d92e8b3ead500dfe6bbf442ef3b8b05ad9094bc3cce16ad7b1a5bb591cf4"],"state_sha256":"61caf0c52d15432c360304b58c5ab3e290d07ae7212c70de0171dd90e2ed93b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G1eL1kok6nIfQBdNxKynZJkIH8Cdhqp7Po3iU2X15/UpEvzOOTfPKiqN07jDmGCiYrmY/WeqmTf2j+1ovmXbDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T07:26:12.115014Z","bundle_sha256":"f9570756ec3d77f98d87ff44b3389e7cf4141cbc72ed045c2fde4675a285f886"}}