{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:SYABN3BGWI3HTQTZ2SKPBT3VZ3","short_pith_number":"pith:SYABN3BG","canonical_record":{"source":{"id":"1403.5215","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-20T17:49:04Z","cross_cats_sorted":["hep-th","math.QA"],"title_canon_sha256":"d04ef53908bfee10c4e9028fc334edeb1135d0525e49ca342d641c72876229a3","abstract_canon_sha256":"6d8c325d82ee09062c81f114ce11fb8ac4afc830122f5561d8fbd82f842d2fb7"},"schema_version":"1.0"},"canonical_sha256":"960016ec26b23679c279d494f0cf75cec95ed4813ea8403f07fe76fe9bfedf2e","source":{"kind":"arxiv","id":"1403.5215","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5215","created_at":"2026-05-18T02:55:57Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5215v1","created_at":"2026-05-18T02:55:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5215","created_at":"2026-05-18T02:55:57Z"},{"alias_kind":"pith_short_12","alias_value":"SYABN3BGWI3H","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SYABN3BGWI3HTQTZ","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SYABN3BG","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:SYABN3BGWI3HTQTZ2SKPBT3VZ3","target":"record","payload":{"canonical_record":{"source":{"id":"1403.5215","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-20T17:49:04Z","cross_cats_sorted":["hep-th","math.QA"],"title_canon_sha256":"d04ef53908bfee10c4e9028fc334edeb1135d0525e49ca342d641c72876229a3","abstract_canon_sha256":"6d8c325d82ee09062c81f114ce11fb8ac4afc830122f5561d8fbd82f842d2fb7"},"schema_version":"1.0"},"canonical_sha256":"960016ec26b23679c279d494f0cf75cec95ed4813ea8403f07fe76fe9bfedf2e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:57.994227Z","signature_b64":"W8J1arD6bu9pDCTA3Kcj2sD5bMuAaWDquYiqS3+F1SvDARua0rIRmgf40t0t/D4rhv9gJNpucQR2HO4sCORXDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"960016ec26b23679c279d494f0cf75cec95ed4813ea8403f07fe76fe9bfedf2e","last_reissued_at":"2026-05-18T02:55:57.993718Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:57.993718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.5215","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":"2026-05-18T02:55:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ATj10iIkSMvCWPcokC7x4S+HkzeNfPrUCxGxfYunE88zS9WVzbYoWnJZGWRvqyS9rI8zcTEOUAwbN9maPKP1Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:28:32.969771Z"},"content_sha256":"39a76284681dcbb97c64b2927bb47e7012ca937bcd3a6061b2a455692c38972e","schema_version":"1.0","event_id":"sha256:39a76284681dcbb97c64b2927bb47e7012ca937bcd3a6061b2a455692c38972e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:SYABN3BGWI3HTQTZ2SKPBT3VZ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Spectral Perspective on Neumann-Zagier","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.QA"],"primary_cat":"math.GT","authors_text":"Roland van der Veen, Tudor Dimofte","submitted_at":"2014-03-20T17:49:04Z","abstract_excerpt":"We provide a new topological interpretation of the symplectic properties of gluing equations for triangulations of hyperbolic 3-manifolds, first discovered by Neumann and Zagier. We also extend the symplectic properties to more general gluings of PGL(2,C) flat connections on the boundaries of 3-manifolds with topological ideal triangulations, proving that gluing is a K_2 symplectic reduction of PGL(2,C) moduli spaces. Recently, such symplectic properties have been central in constructing quantum PGL(2,C) invariants of 3-manifolds. Our methods adapt the spectral network construction of Gaiotto-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5215","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":"2026-05-18T02:55:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JdIe5S8DCN787KddQw+CYj6ukMmt2I/pcitjA70ayzz3vP5xp36LLLzqMbd4wDIuOzOhHZpZpcKI9TOKIoHnCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:28:32.970482Z"},"content_sha256":"428e0808f5236cc3a965af3b07637544f457192b675566c5e9f848c8f2d08f35","schema_version":"1.0","event_id":"sha256:428e0808f5236cc3a965af3b07637544f457192b675566c5e9f848c8f2d08f35"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SYABN3BGWI3HTQTZ2SKPBT3VZ3/bundle.json","state_url":"https://pith.science/pith/SYABN3BGWI3HTQTZ2SKPBT3VZ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SYABN3BGWI3HTQTZ2SKPBT3VZ3/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":"2026-06-06T08:28:32Z","links":{"resolver":"https://pith.science/pith/SYABN3BGWI3HTQTZ2SKPBT3VZ3","bundle":"https://pith.science/pith/SYABN3BGWI3HTQTZ2SKPBT3VZ3/bundle.json","state":"https://pith.science/pith/SYABN3BGWI3HTQTZ2SKPBT3VZ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SYABN3BGWI3HTQTZ2SKPBT3VZ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SYABN3BGWI3HTQTZ2SKPBT3VZ3","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":"6d8c325d82ee09062c81f114ce11fb8ac4afc830122f5561d8fbd82f842d2fb7","cross_cats_sorted":["hep-th","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-20T17:49:04Z","title_canon_sha256":"d04ef53908bfee10c4e9028fc334edeb1135d0525e49ca342d641c72876229a3"},"schema_version":"1.0","source":{"id":"1403.5215","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5215","created_at":"2026-05-18T02:55:57Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5215v1","created_at":"2026-05-18T02:55:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5215","created_at":"2026-05-18T02:55:57Z"},{"alias_kind":"pith_short_12","alias_value":"SYABN3BGWI3H","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SYABN3BGWI3HTQTZ","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SYABN3BG","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:428e0808f5236cc3a965af3b07637544f457192b675566c5e9f848c8f2d08f35","target":"graph","created_at":"2026-05-18T02:55:57Z","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 provide a new topological interpretation of the symplectic properties of gluing equations for triangulations of hyperbolic 3-manifolds, first discovered by Neumann and Zagier. We also extend the symplectic properties to more general gluings of PGL(2,C) flat connections on the boundaries of 3-manifolds with topological ideal triangulations, proving that gluing is a K_2 symplectic reduction of PGL(2,C) moduli spaces. Recently, such symplectic properties have been central in constructing quantum PGL(2,C) invariants of 3-manifolds. Our methods adapt the spectral network construction of Gaiotto-","authors_text":"Roland van der Veen, Tudor Dimofte","cross_cats":["hep-th","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-20T17:49:04Z","title":"A Spectral Perspective on Neumann-Zagier"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5215","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":"sha256:39a76284681dcbb97c64b2927bb47e7012ca937bcd3a6061b2a455692c38972e","target":"record","created_at":"2026-05-18T02:55:57Z","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":"6d8c325d82ee09062c81f114ce11fb8ac4afc830122f5561d8fbd82f842d2fb7","cross_cats_sorted":["hep-th","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-20T17:49:04Z","title_canon_sha256":"d04ef53908bfee10c4e9028fc334edeb1135d0525e49ca342d641c72876229a3"},"schema_version":"1.0","source":{"id":"1403.5215","kind":"arxiv","version":1}},"canonical_sha256":"960016ec26b23679c279d494f0cf75cec95ed4813ea8403f07fe76fe9bfedf2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"960016ec26b23679c279d494f0cf75cec95ed4813ea8403f07fe76fe9bfedf2e","first_computed_at":"2026-05-18T02:55:57.993718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:57.993718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W8J1arD6bu9pDCTA3Kcj2sD5bMuAaWDquYiqS3+F1SvDARua0rIRmgf40t0t/D4rhv9gJNpucQR2HO4sCORXDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:57.994227Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.5215","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39a76284681dcbb97c64b2927bb47e7012ca937bcd3a6061b2a455692c38972e","sha256:428e0808f5236cc3a965af3b07637544f457192b675566c5e9f848c8f2d08f35"],"state_sha256":"f267186507855a8c2236d4322fe4883a66b0ac1a4168fc8aa00bb99d937ba65c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JFhc3SK9BUu2lSp9gyhI7Zp04rGIhnwxKxxmX+BfJslEKInPuXSNAewUfCZNvBv58UvyGq/VLc1XmEH8KrRDDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T08:28:32.974544Z","bundle_sha256":"5fc78018cb460f631664072c28fee9944f6ffd127e4b7cee30fb1e7a993525a6"}}