{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:UN4RRDUMGYC3RIOKYDETRKKTMZ","short_pith_number":"pith:UN4RRDUM","canonical_record":{"source":{"id":"1201.3613","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-01-17T20:31:48Z","cross_cats_sorted":["hep-th","math-ph","math.GT","math.MP"],"title_canon_sha256":"9ff779f673b0c05afb63486cbc3dfd4bf278f3cc18ed24685e54cc53bf370518","abstract_canon_sha256":"ae1a29466aa9617611681c43bf0753f06793a40f574c7102ba02ac08b4086e21"},"schema_version":"1.0"},"canonical_sha256":"a379188e8c3605b8a1cac0c938a953665be684a7070b391219083c44863f05d3","source":{"kind":"arxiv","id":"1201.3613","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3613","created_at":"2026-05-18T01:58:47Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3613v1","created_at":"2026-05-18T01:58:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3613","created_at":"2026-05-18T01:58:47Z"},{"alias_kind":"pith_short_12","alias_value":"UN4RRDUMGYC3","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UN4RRDUMGYC3RIOK","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UN4RRDUM","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:UN4RRDUMGYC3RIOKYDETRKKTMZ","target":"record","payload":{"canonical_record":{"source":{"id":"1201.3613","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-01-17T20:31:48Z","cross_cats_sorted":["hep-th","math-ph","math.GT","math.MP"],"title_canon_sha256":"9ff779f673b0c05afb63486cbc3dfd4bf278f3cc18ed24685e54cc53bf370518","abstract_canon_sha256":"ae1a29466aa9617611681c43bf0753f06793a40f574c7102ba02ac08b4086e21"},"schema_version":"1.0"},"canonical_sha256":"a379188e8c3605b8a1cac0c938a953665be684a7070b391219083c44863f05d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:58:47.942825Z","signature_b64":"X2c9mN+v834nuuOU5SKxWj8oRQgiHYY/ND+obCNCTH1SnnehS/aohTvjxUSFZUuJuKlqQWrQ60SpTeyelfXXBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a379188e8c3605b8a1cac0c938a953665be684a7070b391219083c44863f05d3","last_reissued_at":"2026-05-18T01:58:47.942112Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:58:47.942112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.3613","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":"2026-05-18T01:58:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XPJRjVQh1XjORqcaNOKmz7eZtVHkn1nCH9w85D88GvwIzxUJf2VEZ06VQiaun2nQ6XDYHPQFtvff2WZTZiSXDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:35:29.822257Z"},"content_sha256":"a4b6baf328bc36c450fe4613adfa7d60d66633951376765dfff89af773813fcd","schema_version":"1.0","event_id":"sha256:a4b6baf328bc36c450fe4613adfa7d60d66633951376765dfff89af773813fcd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:UN4RRDUMGYC3RIOKYDETRKKTMZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the exact evaluation of spin networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.GT","math.MP"],"primary_cat":"gr-qc","authors_text":"Jeff Hnybida, Laurent Freidel","submitted_at":"2012-01-17T20:31:48Z","abstract_excerpt":"We introduce a fully coherent spin network amplitude whose expansion generates all SU(2) spin networks associated with a given graph. We then give an explicit evaluation of this amplitude for an arbitrary graph. We show how this coherent amplitude can be obtained from the specialization of a generating functional obtained by the contraction of parametrized intertwiners a la Schwinger. We finally give the explicit evaluation of this generating functional for arbitrary graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3613","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":"2026-05-18T01:58:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aOGHBOKtUl4WZ7/GZicd6m3mJQtmBtG1zQ76NkTr/WHTK+q31IgldgXCMTcE4UVBS6M+AsaSuzwYl7w6tnWnAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:35:29.822928Z"},"content_sha256":"07addcebeba85d0ebd89afc3ee17568c07d5bbd9325f12e8ecb4d9457f4bfcc7","schema_version":"1.0","event_id":"sha256:07addcebeba85d0ebd89afc3ee17568c07d5bbd9325f12e8ecb4d9457f4bfcc7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UN4RRDUMGYC3RIOKYDETRKKTMZ/bundle.json","state_url":"https://pith.science/pith/UN4RRDUMGYC3RIOKYDETRKKTMZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UN4RRDUMGYC3RIOKYDETRKKTMZ/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":"2026-05-27T05:35:29Z","links":{"resolver":"https://pith.science/pith/UN4RRDUMGYC3RIOKYDETRKKTMZ","bundle":"https://pith.science/pith/UN4RRDUMGYC3RIOKYDETRKKTMZ/bundle.json","state":"https://pith.science/pith/UN4RRDUMGYC3RIOKYDETRKKTMZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UN4RRDUMGYC3RIOKYDETRKKTMZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UN4RRDUMGYC3RIOKYDETRKKTMZ","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":"ae1a29466aa9617611681c43bf0753f06793a40f574c7102ba02ac08b4086e21","cross_cats_sorted":["hep-th","math-ph","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-01-17T20:31:48Z","title_canon_sha256":"9ff779f673b0c05afb63486cbc3dfd4bf278f3cc18ed24685e54cc53bf370518"},"schema_version":"1.0","source":{"id":"1201.3613","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3613","created_at":"2026-05-18T01:58:47Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3613v1","created_at":"2026-05-18T01:58:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3613","created_at":"2026-05-18T01:58:47Z"},{"alias_kind":"pith_short_12","alias_value":"UN4RRDUMGYC3","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UN4RRDUMGYC3RIOK","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UN4RRDUM","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:07addcebeba85d0ebd89afc3ee17568c07d5bbd9325f12e8ecb4d9457f4bfcc7","target":"graph","created_at":"2026-05-18T01:58:47Z","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 introduce a fully coherent spin network amplitude whose expansion generates all SU(2) spin networks associated with a given graph. We then give an explicit evaluation of this amplitude for an arbitrary graph. We show how this coherent amplitude can be obtained from the specialization of a generating functional obtained by the contraction of parametrized intertwiners a la Schwinger. We finally give the explicit evaluation of this generating functional for arbitrary graphs.","authors_text":"Jeff Hnybida, Laurent Freidel","cross_cats":["hep-th","math-ph","math.GT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-01-17T20:31:48Z","title":"On the exact evaluation of spin networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3613","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:a4b6baf328bc36c450fe4613adfa7d60d66633951376765dfff89af773813fcd","target":"record","created_at":"2026-05-18T01:58:47Z","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":"ae1a29466aa9617611681c43bf0753f06793a40f574c7102ba02ac08b4086e21","cross_cats_sorted":["hep-th","math-ph","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-01-17T20:31:48Z","title_canon_sha256":"9ff779f673b0c05afb63486cbc3dfd4bf278f3cc18ed24685e54cc53bf370518"},"schema_version":"1.0","source":{"id":"1201.3613","kind":"arxiv","version":1}},"canonical_sha256":"a379188e8c3605b8a1cac0c938a953665be684a7070b391219083c44863f05d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a379188e8c3605b8a1cac0c938a953665be684a7070b391219083c44863f05d3","first_computed_at":"2026-05-18T01:58:47.942112Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:47.942112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X2c9mN+v834nuuOU5SKxWj8oRQgiHYY/ND+obCNCTH1SnnehS/aohTvjxUSFZUuJuKlqQWrQ60SpTeyelfXXBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:47.942825Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.3613","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4b6baf328bc36c450fe4613adfa7d60d66633951376765dfff89af773813fcd","sha256:07addcebeba85d0ebd89afc3ee17568c07d5bbd9325f12e8ecb4d9457f4bfcc7"],"state_sha256":"4c192db61831190869cf9e9a572825f70a2d587c9582adb81c306f73d1f39346"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u507G4m3Q/RLEDbQtw5uSQlWaWjS3pTAgOMOhMImunsEaP4X17x2WtGZIL1XuDrKunYY2Ti/Y+90tp/S8aKtAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T05:35:29.826822Z","bundle_sha256":"f1f78c71bbb4bcbdd18a6e70973b46b145a50633c9f641b4776f68d03ade8392"}}