{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:FNM6IIYM4YLLL5KT5JK2T56GSL","short_pith_number":"pith:FNM6IIYM","canonical_record":{"source":{"id":"1010.4787","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-10-22T19:43:16Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"fddf8d67f7387654eacb9f7135b3dfa6c3d655c8de24ce02a70a2ac0ba31dc5b","abstract_canon_sha256":"bd7d82ce46d7266871241026fe85d6f48a6a15e82f87ca49ba116f5c4b132165"},"schema_version":"1.0"},"canonical_sha256":"2b59e4230ce616b5f553ea55a9f7c692ff5450bf34367e661342badf4ba4ce6a","source":{"kind":"arxiv","id":"1010.4787","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.4787","created_at":"2026-05-18T04:24:45Z"},{"alias_kind":"arxiv_version","alias_value":"1010.4787v1","created_at":"2026-05-18T04:24:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4787","created_at":"2026-05-18T04:24:45Z"},{"alias_kind":"pith_short_12","alias_value":"FNM6IIYM4YLL","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FNM6IIYM4YLLL5KT","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FNM6IIYM","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:FNM6IIYM4YLLL5KT5JK2T56GSL","target":"record","payload":{"canonical_record":{"source":{"id":"1010.4787","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-10-22T19:43:16Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"fddf8d67f7387654eacb9f7135b3dfa6c3d655c8de24ce02a70a2ac0ba31dc5b","abstract_canon_sha256":"bd7d82ce46d7266871241026fe85d6f48a6a15e82f87ca49ba116f5c4b132165"},"schema_version":"1.0"},"canonical_sha256":"2b59e4230ce616b5f553ea55a9f7c692ff5450bf34367e661342badf4ba4ce6a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:45.176335Z","signature_b64":"x4Svu09L4C6UJxI4W/YoSzMYHhwK2Ih8Uz0KzXYl4w1ftrUizrBajcAlyj997CuLi/N4Iu+mx91OaZPfxouVAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b59e4230ce616b5f553ea55a9f7c692ff5450bf34367e661342badf4ba4ce6a","last_reissued_at":"2026-05-18T04:24:45.175962Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:45.175962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.4787","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":"2026-05-18T04:24:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZUxXeIMAALdpmDzrxgcg9qNtpude4YWfeSlpM9s7lNeUwZUOwIoxGjHKsIBv089xwyuC0B5KkqFfoAMFsmgNCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:19:56.901812Z"},"content_sha256":"e12ed3752482ccebfcf7d9bf67f2237bbad20122fa199ea3f7173ff09fd56442","schema_version":"1.0","event_id":"sha256:e12ed3752482ccebfcf7d9bf67f2237bbad20122fa199ea3f7173ff09fd56442"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:FNM6IIYM4YLLL5KT5JK2T56GSL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Operator Spin Foam Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Benjamin Bahr, Frank Hellmann, Jerzy lewandowski, Marcin Kisielowski, Wojciech Kami\\'nski","submitted_at":"2010-10-22T19:43:16Z","abstract_excerpt":"The goal of this paper is to introduce a systematic approach to spin foams. We define operator spin foams, that is foams labelled by group representations and operators, as the main tool. An equivalence relation we impose in the set of the operator spin foams allows to split the faces and the edges of the foams. The consistency with that relation requires introduction of the (familiar for the BF theory) face amplitude. The operator spin foam models are defined quite generally. Imposing a maximal symmetry leads to a family we call natural operator spin foam models. This symmetry, combined with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4787","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":"2026-05-18T04:24:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BKO1AjU4AO8w5yaztEcFztK4mUrDis6dW62zBq1h5VF7MJivDzw56jQj3Nnr7s1ZED6MUO9bWF67aH9EudkUDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:19:56.902517Z"},"content_sha256":"3838470ddb13603c7740afbe0d4992bf368a8cf4da6e2770e3cf4057047a4afa","schema_version":"1.0","event_id":"sha256:3838470ddb13603c7740afbe0d4992bf368a8cf4da6e2770e3cf4057047a4afa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FNM6IIYM4YLLL5KT5JK2T56GSL/bundle.json","state_url":"https://pith.science/pith/FNM6IIYM4YLLL5KT5JK2T56GSL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FNM6IIYM4YLLL5KT5JK2T56GSL/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":"2026-05-26T12:19:56Z","links":{"resolver":"https://pith.science/pith/FNM6IIYM4YLLL5KT5JK2T56GSL","bundle":"https://pith.science/pith/FNM6IIYM4YLLL5KT5JK2T56GSL/bundle.json","state":"https://pith.science/pith/FNM6IIYM4YLLL5KT5JK2T56GSL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FNM6IIYM4YLLL5KT5JK2T56GSL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:FNM6IIYM4YLLL5KT5JK2T56GSL","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":"bd7d82ce46d7266871241026fe85d6f48a6a15e82f87ca49ba116f5c4b132165","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-10-22T19:43:16Z","title_canon_sha256":"fddf8d67f7387654eacb9f7135b3dfa6c3d655c8de24ce02a70a2ac0ba31dc5b"},"schema_version":"1.0","source":{"id":"1010.4787","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.4787","created_at":"2026-05-18T04:24:45Z"},{"alias_kind":"arxiv_version","alias_value":"1010.4787v1","created_at":"2026-05-18T04:24:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4787","created_at":"2026-05-18T04:24:45Z"},{"alias_kind":"pith_short_12","alias_value":"FNM6IIYM4YLL","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FNM6IIYM4YLLL5KT","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FNM6IIYM","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:3838470ddb13603c7740afbe0d4992bf368a8cf4da6e2770e3cf4057047a4afa","target":"graph","created_at":"2026-05-18T04:24:45Z","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":"The goal of this paper is to introduce a systematic approach to spin foams. We define operator spin foams, that is foams labelled by group representations and operators, as the main tool. An equivalence relation we impose in the set of the operator spin foams allows to split the faces and the edges of the foams. The consistency with that relation requires introduction of the (familiar for the BF theory) face amplitude. The operator spin foam models are defined quite generally. Imposing a maximal symmetry leads to a family we call natural operator spin foam models. This symmetry, combined with ","authors_text":"Benjamin Bahr, Frank Hellmann, Jerzy lewandowski, Marcin Kisielowski, Wojciech Kami\\'nski","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-10-22T19:43:16Z","title":"Operator Spin Foam Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4787","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:e12ed3752482ccebfcf7d9bf67f2237bbad20122fa199ea3f7173ff09fd56442","target":"record","created_at":"2026-05-18T04:24:45Z","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":"bd7d82ce46d7266871241026fe85d6f48a6a15e82f87ca49ba116f5c4b132165","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-10-22T19:43:16Z","title_canon_sha256":"fddf8d67f7387654eacb9f7135b3dfa6c3d655c8de24ce02a70a2ac0ba31dc5b"},"schema_version":"1.0","source":{"id":"1010.4787","kind":"arxiv","version":1}},"canonical_sha256":"2b59e4230ce616b5f553ea55a9f7c692ff5450bf34367e661342badf4ba4ce6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b59e4230ce616b5f553ea55a9f7c692ff5450bf34367e661342badf4ba4ce6a","first_computed_at":"2026-05-18T04:24:45.175962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:45.175962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x4Svu09L4C6UJxI4W/YoSzMYHhwK2Ih8Uz0KzXYl4w1ftrUizrBajcAlyj997CuLi/N4Iu+mx91OaZPfxouVAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:45.176335Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.4787","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e12ed3752482ccebfcf7d9bf67f2237bbad20122fa199ea3f7173ff09fd56442","sha256:3838470ddb13603c7740afbe0d4992bf368a8cf4da6e2770e3cf4057047a4afa"],"state_sha256":"6fa67f3bf22d75be5e4a4dc9ba031fc6e5559328ad8683bfb3473d6bb7b17d2a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JS2fGuDnznGscvkaJMBfl28DSACT/F1ywLR+q3ZTVzBGFTwwzBhcrat+MSspxQsigOkujAr1gDhG+6QicPF0AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T12:19:56.906448Z","bundle_sha256":"e962b6ee2e16eed91e8a7cb4f40bfa4b35fb3ec35f709cba84156a62a9d1c74e"}}