{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:BVBWLRH2VPHGGN2I6WHIHHQOGY","short_pith_number":"pith:BVBWLRH2","canonical_record":{"source":{"id":"1909.07937","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2019-09-17T17:15:53Z","cross_cats_sorted":["hep-th","math-ph","math.MP","quant-ph"],"title_canon_sha256":"42fc0ad7523c0192d93f50450fd1048ba9114b6ff60541f7ce2e2bf73486ad66","abstract_canon_sha256":"bb4856a94c015a6113fc73b36a33b14f730d76ba364b7e71f635c9686aece4f6"},"schema_version":"1.0"},"canonical_sha256":"0d4365c4faabce633748f58e839e0e362e259f1575b177a0a7c50eddb8c5284b","source":{"kind":"arxiv","id":"1909.07937","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.07937","created_at":"2026-07-05T00:41:38Z"},{"alias_kind":"arxiv_version","alias_value":"1909.07937v1","created_at":"2026-07-05T00:41:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.07937","created_at":"2026-07-05T00:41:38Z"},{"alias_kind":"pith_short_12","alias_value":"BVBWLRH2VPHG","created_at":"2026-07-05T00:41:38Z"},{"alias_kind":"pith_short_16","alias_value":"BVBWLRH2VPHGGN2I","created_at":"2026-07-05T00:41:38Z"},{"alias_kind":"pith_short_8","alias_value":"BVBWLRH2","created_at":"2026-07-05T00:41:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:BVBWLRH2VPHGGN2I6WHIHHQOGY","target":"record","payload":{"canonical_record":{"source":{"id":"1909.07937","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2019-09-17T17:15:53Z","cross_cats_sorted":["hep-th","math-ph","math.MP","quant-ph"],"title_canon_sha256":"42fc0ad7523c0192d93f50450fd1048ba9114b6ff60541f7ce2e2bf73486ad66","abstract_canon_sha256":"bb4856a94c015a6113fc73b36a33b14f730d76ba364b7e71f635c9686aece4f6"},"schema_version":"1.0"},"canonical_sha256":"0d4365c4faabce633748f58e839e0e362e259f1575b177a0a7c50eddb8c5284b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:41:38.499525Z","signature_b64":"ARioEVGByeAfXYV0uySnyVWpSCf/PWyJlV85kPNXDCCGtFOXYIcSRtwQZVtDfC3BhBqvLB/KeNUeI1Tzg7s9Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d4365c4faabce633748f58e839e0e362e259f1575b177a0a7c50eddb8c5284b","last_reissued_at":"2026-07-05T00:41:38.499108Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:41:38.499108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1909.07937","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":"2026-07-05T00:41:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SNeLSqLngjlRBsvHZZrn5APIaDox+cD7AFZCiRjBIL1NacSGfFhwFePqWgekDRo8TLN5M8wSOYijLCnEkmpdCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T11:05:10.998941Z"},"content_sha256":"2d01a59c0ae8d1d2d7cae5f8b4f5e499a7c89e74134cb1f640df30c93117cf2f","schema_version":"1.0","event_id":"sha256:2d01a59c0ae8d1d2d7cae5f8b4f5e499a7c89e74134cb1f640df30c93117cf2f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:BVBWLRH2VPHGGN2I6WHIHHQOGY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Excitations in strict 2-group higher gauge models of topological phases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Alex Bullivant, Clement Delcamp","submitted_at":"2019-09-17T17:15:53Z","abstract_excerpt":"We consider an exactly solvable model for topological phases in (3+1)d whose input data is a strict 2-group. This model, which has a higher gauge theory interpretation, provides a lattice Hamiltonian realisation of the Yetter homotopy 2-type topological quantum field theory. The Hamiltonian yields bulk flux and charge composite excitations that are either point-like or loop-like. Applying a generalised tube algebra approach, we reveal the algebraic structure underlying these excitations and derive the irreducible modules of this algebra, which in turn classify the elementary excitations of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.07937","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1909.07937/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:41:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ScQ3JzB1DcM0GJ1hbMyW2KQzps+UwlMavzcwEZVeB7nLx5VdfkZkk4GVWP2HGMM9uQ5XNvMq5ZBf9IrT3fwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T11:05:10.999451Z"},"content_sha256":"8c3315ced18c73daa8d3b6120fe2e4463625538ad0293c2bcddcae9e8b651d92","schema_version":"1.0","event_id":"sha256:8c3315ced18c73daa8d3b6120fe2e4463625538ad0293c2bcddcae9e8b651d92"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BVBWLRH2VPHGGN2I6WHIHHQOGY/bundle.json","state_url":"https://pith.science/pith/BVBWLRH2VPHGGN2I6WHIHHQOGY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BVBWLRH2VPHGGN2I6WHIHHQOGY/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":"2026-08-04T11:05:11Z","links":{"resolver":"https://pith.science/pith/BVBWLRH2VPHGGN2I6WHIHHQOGY","bundle":"https://pith.science/pith/BVBWLRH2VPHGGN2I6WHIHHQOGY/bundle.json","state":"https://pith.science/pith/BVBWLRH2VPHGGN2I6WHIHHQOGY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BVBWLRH2VPHGGN2I6WHIHHQOGY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:BVBWLRH2VPHGGN2I6WHIHHQOGY","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":"bb4856a94c015a6113fc73b36a33b14f730d76ba364b7e71f635c9686aece4f6","cross_cats_sorted":["hep-th","math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2019-09-17T17:15:53Z","title_canon_sha256":"42fc0ad7523c0192d93f50450fd1048ba9114b6ff60541f7ce2e2bf73486ad66"},"schema_version":"1.0","source":{"id":"1909.07937","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.07937","created_at":"2026-07-05T00:41:38Z"},{"alias_kind":"arxiv_version","alias_value":"1909.07937v1","created_at":"2026-07-05T00:41:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.07937","created_at":"2026-07-05T00:41:38Z"},{"alias_kind":"pith_short_12","alias_value":"BVBWLRH2VPHG","created_at":"2026-07-05T00:41:38Z"},{"alias_kind":"pith_short_16","alias_value":"BVBWLRH2VPHGGN2I","created_at":"2026-07-05T00:41:38Z"},{"alias_kind":"pith_short_8","alias_value":"BVBWLRH2","created_at":"2026-07-05T00:41:38Z"}],"graph_snapshots":[{"event_id":"sha256:8c3315ced18c73daa8d3b6120fe2e4463625538ad0293c2bcddcae9e8b651d92","target":"graph","created_at":"2026-07-05T00:41:38Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1909.07937/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider an exactly solvable model for topological phases in (3+1)d whose input data is a strict 2-group. This model, which has a higher gauge theory interpretation, provides a lattice Hamiltonian realisation of the Yetter homotopy 2-type topological quantum field theory. The Hamiltonian yields bulk flux and charge composite excitations that are either point-like or loop-like. Applying a generalised tube algebra approach, we reveal the algebraic structure underlying these excitations and derive the irreducible modules of this algebra, which in turn classify the elementary excitations of the","authors_text":"Alex Bullivant, Clement Delcamp","cross_cats":["hep-th","math-ph","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2019-09-17T17:15:53Z","title":"Excitations in strict 2-group higher gauge models of topological phases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.07937","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":"sha256:2d01a59c0ae8d1d2d7cae5f8b4f5e499a7c89e74134cb1f640df30c93117cf2f","target":"record","created_at":"2026-07-05T00:41:38Z","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":"bb4856a94c015a6113fc73b36a33b14f730d76ba364b7e71f635c9686aece4f6","cross_cats_sorted":["hep-th","math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2019-09-17T17:15:53Z","title_canon_sha256":"42fc0ad7523c0192d93f50450fd1048ba9114b6ff60541f7ce2e2bf73486ad66"},"schema_version":"1.0","source":{"id":"1909.07937","kind":"arxiv","version":1}},"canonical_sha256":"0d4365c4faabce633748f58e839e0e362e259f1575b177a0a7c50eddb8c5284b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d4365c4faabce633748f58e839e0e362e259f1575b177a0a7c50eddb8c5284b","first_computed_at":"2026-07-05T00:41:38.499108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:41:38.499108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ARioEVGByeAfXYV0uySnyVWpSCf/PWyJlV85kPNXDCCGtFOXYIcSRtwQZVtDfC3BhBqvLB/KeNUeI1Tzg7s9Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:41:38.499525Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.07937","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d01a59c0ae8d1d2d7cae5f8b4f5e499a7c89e74134cb1f640df30c93117cf2f","sha256:8c3315ced18c73daa8d3b6120fe2e4463625538ad0293c2bcddcae9e8b651d92"],"state_sha256":"d983ab7654048a5520a3f13bd47a7c1a8d3a0eb232bff68c95eba5983aa6b29e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k+Oasf1g1CrQn0IjcCDcEPo7WZ3Zd3XnnD01igp3ZsbwSaC+bVfj5e7x+sTkDnm3EA5hUlpidT6NgpMBFzKiDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T11:05:11.003915Z","bundle_sha256":"12236af9c90cf9f8111d4cfd5fe9d6544db630122d23aed89d6a178ceb821378"}}