{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WGJ3P27PRIJFOSDBORSEXIVE2M","short_pith_number":"pith:WGJ3P27P","canonical_record":{"source":{"id":"1506.01774","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-06-05T04:32:04Z","cross_cats_sorted":[],"title_canon_sha256":"1d1c40b4c6d97efae91113fe1505657dec7e9b0342ef1791881ce92f15aea5f4","abstract_canon_sha256":"b422fe2ca1f3a4dcd7aa8bf2326ea772726e117bcc6e616ec5883237469ea073"},"schema_version":"1.0"},"canonical_sha256":"b193b7ebef8a1257486174644ba2a4d3040e368cf33a0eeb1f327af0712deac5","source":{"kind":"arxiv","id":"1506.01774","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01774","created_at":"2026-05-18T01:32:00Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01774v2","created_at":"2026-05-18T01:32:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01774","created_at":"2026-05-18T01:32:00Z"},{"alias_kind":"pith_short_12","alias_value":"WGJ3P27PRIJF","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WGJ3P27PRIJFOSDB","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WGJ3P27P","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WGJ3P27PRIJFOSDBORSEXIVE2M","target":"record","payload":{"canonical_record":{"source":{"id":"1506.01774","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-06-05T04:32:04Z","cross_cats_sorted":[],"title_canon_sha256":"1d1c40b4c6d97efae91113fe1505657dec7e9b0342ef1791881ce92f15aea5f4","abstract_canon_sha256":"b422fe2ca1f3a4dcd7aa8bf2326ea772726e117bcc6e616ec5883237469ea073"},"schema_version":"1.0"},"canonical_sha256":"b193b7ebef8a1257486174644ba2a4d3040e368cf33a0eeb1f327af0712deac5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:00.391622Z","signature_b64":"he0VaSoyL5pGMHG9dwIwNfpnhdl9AwYTfgnxpIdA+TZHbKWZZo2h/2S0PBUQjGuSrfugYo5bhJOeF6qsXRsCCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b193b7ebef8a1257486174644ba2a4d3040e368cf33a0eeb1f327af0712deac5","last_reissued_at":"2026-05-18T01:32:00.391111Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:00.391111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.01774","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":"2026-05-18T01:32:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z8kt5UTdm8fYip6Y0ORnjqqaOtkZdfr2YLsVCZzts0AUjAwPwnu6d35syb+NXz67gJ1yOOL4WLPGexaZ9rTFAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:10:37.887876Z"},"content_sha256":"474b38e998f00c716cd0abfa08c6aa32ee53d10abbd6eb00d25c18eb710772dd","schema_version":"1.0","event_id":"sha256:474b38e998f00c716cd0abfa08c6aa32ee53d10abbd6eb00d25c18eb710772dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WGJ3P27PRIJFOSDBORSEXIVE2M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A polynomial defined by the SL(2;C)-Reidemeister torsion for a homology 3-sphere obtained by a Dehn surgery along a (2p,q)-torus knot","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Teruaki Kitano","submitted_at":"2015-06-05T04:32:04Z","abstract_excerpt":"Let K be a (2p,q)-torus knot and M_n is a 3-manifold obtained by 1/n-Dehn surgery along K. We consider a polynomial whose zeros are the inverses of the Reideimeister torsion of M_n for SL(2;C)-irreducible representations. Johnson gave a formula for the case of the (2,3)-torus knot under some modification and normalization. We generalize this formula by using Tchebychev polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01774","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":"2026-05-18T01:32:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2vzGXOw68DQ+elXNzqzWOMHPQr7KfILQkNJP6lrOm9R+bctpY9WPh6UM8+pZrxVxheh210OblsHE8pcxLo9yDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:10:37.888476Z"},"content_sha256":"7832aef99b2e03b49fffe800b1b1619ac00d8fb4d5905faf89dded1727d74053","schema_version":"1.0","event_id":"sha256:7832aef99b2e03b49fffe800b1b1619ac00d8fb4d5905faf89dded1727d74053"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WGJ3P27PRIJFOSDBORSEXIVE2M/bundle.json","state_url":"https://pith.science/pith/WGJ3P27PRIJFOSDBORSEXIVE2M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WGJ3P27PRIJFOSDBORSEXIVE2M/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":"2026-06-01T08:10:37Z","links":{"resolver":"https://pith.science/pith/WGJ3P27PRIJFOSDBORSEXIVE2M","bundle":"https://pith.science/pith/WGJ3P27PRIJFOSDBORSEXIVE2M/bundle.json","state":"https://pith.science/pith/WGJ3P27PRIJFOSDBORSEXIVE2M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WGJ3P27PRIJFOSDBORSEXIVE2M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WGJ3P27PRIJFOSDBORSEXIVE2M","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":"b422fe2ca1f3a4dcd7aa8bf2326ea772726e117bcc6e616ec5883237469ea073","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-06-05T04:32:04Z","title_canon_sha256":"1d1c40b4c6d97efae91113fe1505657dec7e9b0342ef1791881ce92f15aea5f4"},"schema_version":"1.0","source":{"id":"1506.01774","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.01774","created_at":"2026-05-18T01:32:00Z"},{"alias_kind":"arxiv_version","alias_value":"1506.01774v2","created_at":"2026-05-18T01:32:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01774","created_at":"2026-05-18T01:32:00Z"},{"alias_kind":"pith_short_12","alias_value":"WGJ3P27PRIJF","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WGJ3P27PRIJFOSDB","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WGJ3P27P","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:7832aef99b2e03b49fffe800b1b1619ac00d8fb4d5905faf89dded1727d74053","target":"graph","created_at":"2026-05-18T01:32:00Z","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":"Let K be a (2p,q)-torus knot and M_n is a 3-manifold obtained by 1/n-Dehn surgery along K. We consider a polynomial whose zeros are the inverses of the Reideimeister torsion of M_n for SL(2;C)-irreducible representations. Johnson gave a formula for the case of the (2,3)-torus knot under some modification and normalization. We generalize this formula by using Tchebychev polynomials.","authors_text":"Teruaki Kitano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-06-05T04:32:04Z","title":"A polynomial defined by the SL(2;C)-Reidemeister torsion for a homology 3-sphere obtained by a Dehn surgery along a (2p,q)-torus knot"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01774","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":"sha256:474b38e998f00c716cd0abfa08c6aa32ee53d10abbd6eb00d25c18eb710772dd","target":"record","created_at":"2026-05-18T01:32:00Z","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":"b422fe2ca1f3a4dcd7aa8bf2326ea772726e117bcc6e616ec5883237469ea073","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-06-05T04:32:04Z","title_canon_sha256":"1d1c40b4c6d97efae91113fe1505657dec7e9b0342ef1791881ce92f15aea5f4"},"schema_version":"1.0","source":{"id":"1506.01774","kind":"arxiv","version":2}},"canonical_sha256":"b193b7ebef8a1257486174644ba2a4d3040e368cf33a0eeb1f327af0712deac5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b193b7ebef8a1257486174644ba2a4d3040e368cf33a0eeb1f327af0712deac5","first_computed_at":"2026-05-18T01:32:00.391111Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:00.391111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"he0VaSoyL5pGMHG9dwIwNfpnhdl9AwYTfgnxpIdA+TZHbKWZZo2h/2S0PBUQjGuSrfugYo5bhJOeF6qsXRsCCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:00.391622Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.01774","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:474b38e998f00c716cd0abfa08c6aa32ee53d10abbd6eb00d25c18eb710772dd","sha256:7832aef99b2e03b49fffe800b1b1619ac00d8fb4d5905faf89dded1727d74053"],"state_sha256":"1eb79b24d80f866b95a12102b14a9000d5bd6a08622e313394d6577ef53f4035"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vb7/okpsY5J5oPg6I2DFVRbyrQZ8zzfFWe/z/K0AyeanWYBNBWIfrFEoHXfamLj/PG/Dzmo400/iPUUMGa72AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T08:10:37.890678Z","bundle_sha256":"823b47f9f5f748141f9948ecbcb96c2274f74a22f3deb96112327af859262ecb"}}