{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:XCCYQ2KZDOCVNC664TYFNDZ2SZ","short_pith_number":"pith:XCCYQ2KZ","canonical_record":{"source":{"id":"2001.11938","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2020-01-31T16:28:31Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"2f975b32a043bb8eff423d0711e8fd990930c535fede63d50481a208617f2e36","abstract_canon_sha256":"3b2a1e9a79164e8ffd1e5f98d6a84caf68def00f6bcb602fdd7c617f001a6689"},"schema_version":"1.0"},"canonical_sha256":"b8858869591b85568bdee4f0568f3a96665bf53d656e79b00008a2700ce469a8","source":{"kind":"arxiv","id":"2001.11938","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2001.11938","created_at":"2026-07-05T01:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"2001.11938v2","created_at":"2026-07-05T01:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.11938","created_at":"2026-07-05T01:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"XCCYQ2KZDOCV","created_at":"2026-07-05T01:14:36Z"},{"alias_kind":"pith_short_16","alias_value":"XCCYQ2KZDOCVNC66","created_at":"2026-07-05T01:14:36Z"},{"alias_kind":"pith_short_8","alias_value":"XCCYQ2KZ","created_at":"2026-07-05T01:14:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:XCCYQ2KZDOCVNC664TYFNDZ2SZ","target":"record","payload":{"canonical_record":{"source":{"id":"2001.11938","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2020-01-31T16:28:31Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"2f975b32a043bb8eff423d0711e8fd990930c535fede63d50481a208617f2e36","abstract_canon_sha256":"3b2a1e9a79164e8ffd1e5f98d6a84caf68def00f6bcb602fdd7c617f001a6689"},"schema_version":"1.0"},"canonical_sha256":"b8858869591b85568bdee4f0568f3a96665bf53d656e79b00008a2700ce469a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:14:36.688638Z","signature_b64":"O4JundxIfyoRO5GKryrxmCogBcxtMmh0Rw3HNxFdeNMCcD2krMqv3m+GIMaHIuA/Lbyc9typSvS3uG9f+TYKAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8858869591b85568bdee4f0568f3a96665bf53d656e79b00008a2700ce469a8","last_reissued_at":"2026-07-05T01:14:36.688132Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:14:36.688132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2001.11938","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":"2026-07-05T01:14:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pHK7O0QMY0Mxm0dZSk/sIh+iz7mtCQhvDHe7XiBzbwpV+yxemIEcnW8wdpY10bNqvRxtDXoMJulK0YHr1Db6AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T12:24:43.809466Z"},"content_sha256":"4c00598c8c53096d492e6807f4cdbab4403a08b39ece24832425bdb4b0831842","schema_version":"1.0","event_id":"sha256:4c00598c8c53096d492e6807f4cdbab4403a08b39ece24832425bdb4b0831842"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:XCCYQ2KZDOCVNC664TYFNDZ2SZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"TQFT, Symmetry Breaking, and Finite Gauge Theory in 3+1D","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"cond-mat.str-el","authors_text":"Ryan Thorngren","submitted_at":"2020-01-31T16:28:31Z","abstract_excerpt":"We derive a canonical form for 2-group gauge theory in 3+1D which shows they are either equivalent to Dijkgraaf-Witten theory or to the so-called \"EF1\" topological order of Lan-Wen. According to that classification, recently argued from a different point of view by Johnson-Freyd, this amounts to a very large class of all 3+1D TQFTs. We use this canonical form to compute all possible anomalies of 2-group gauge theory which may occur without spontaneous symmetry breaking, providing a converse of the recent symmetry-enforced-gaplessness constraints of C\\'ordova-Ohmori and also uncovering some pos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.11938","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2001.11938/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":"2026-07-05T01:14:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Azg1xSu785D0Vh3u7XZO0v0fEZ0m09cJc0bh6V+e/UfH02mTjIySPG7ij8tPmVZ/uhisxNTxSETvFyvZRvlQDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T12:24:43.810028Z"},"content_sha256":"ef4c1280e11c1f5d27cc8b6abb613ba449a9d707e217c9aaa494d74900b40031","schema_version":"1.0","event_id":"sha256:ef4c1280e11c1f5d27cc8b6abb613ba449a9d707e217c9aaa494d74900b40031"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XCCYQ2KZDOCVNC664TYFNDZ2SZ/bundle.json","state_url":"https://pith.science/pith/XCCYQ2KZDOCVNC664TYFNDZ2SZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XCCYQ2KZDOCVNC664TYFNDZ2SZ/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":"2026-08-16T12:24:43Z","links":{"resolver":"https://pith.science/pith/XCCYQ2KZDOCVNC664TYFNDZ2SZ","bundle":"https://pith.science/pith/XCCYQ2KZDOCVNC664TYFNDZ2SZ/bundle.json","state":"https://pith.science/pith/XCCYQ2KZDOCVNC664TYFNDZ2SZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XCCYQ2KZDOCVNC664TYFNDZ2SZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:XCCYQ2KZDOCVNC664TYFNDZ2SZ","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":"3b2a1e9a79164e8ffd1e5f98d6a84caf68def00f6bcb602fdd7c617f001a6689","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2020-01-31T16:28:31Z","title_canon_sha256":"2f975b32a043bb8eff423d0711e8fd990930c535fede63d50481a208617f2e36"},"schema_version":"1.0","source":{"id":"2001.11938","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2001.11938","created_at":"2026-07-05T01:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"2001.11938v2","created_at":"2026-07-05T01:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.11938","created_at":"2026-07-05T01:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"XCCYQ2KZDOCV","created_at":"2026-07-05T01:14:36Z"},{"alias_kind":"pith_short_16","alias_value":"XCCYQ2KZDOCVNC66","created_at":"2026-07-05T01:14:36Z"},{"alias_kind":"pith_short_8","alias_value":"XCCYQ2KZ","created_at":"2026-07-05T01:14:36Z"}],"graph_snapshots":[{"event_id":"sha256:ef4c1280e11c1f5d27cc8b6abb613ba449a9d707e217c9aaa494d74900b40031","target":"graph","created_at":"2026-07-05T01:14:36Z","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/2001.11938/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive a canonical form for 2-group gauge theory in 3+1D which shows they are either equivalent to Dijkgraaf-Witten theory or to the so-called \"EF1\" topological order of Lan-Wen. According to that classification, recently argued from a different point of view by Johnson-Freyd, this amounts to a very large class of all 3+1D TQFTs. We use this canonical form to compute all possible anomalies of 2-group gauge theory which may occur without spontaneous symmetry breaking, providing a converse of the recent symmetry-enforced-gaplessness constraints of C\\'ordova-Ohmori and also uncovering some pos","authors_text":"Ryan Thorngren","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2020-01-31T16:28:31Z","title":"TQFT, Symmetry Breaking, and Finite Gauge Theory in 3+1D"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.11938","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":"sha256:4c00598c8c53096d492e6807f4cdbab4403a08b39ece24832425bdb4b0831842","target":"record","created_at":"2026-07-05T01:14:36Z","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":"3b2a1e9a79164e8ffd1e5f98d6a84caf68def00f6bcb602fdd7c617f001a6689","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2020-01-31T16:28:31Z","title_canon_sha256":"2f975b32a043bb8eff423d0711e8fd990930c535fede63d50481a208617f2e36"},"schema_version":"1.0","source":{"id":"2001.11938","kind":"arxiv","version":2}},"canonical_sha256":"b8858869591b85568bdee4f0568f3a96665bf53d656e79b00008a2700ce469a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8858869591b85568bdee4f0568f3a96665bf53d656e79b00008a2700ce469a8","first_computed_at":"2026-07-05T01:14:36.688132Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:14:36.688132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O4JundxIfyoRO5GKryrxmCogBcxtMmh0Rw3HNxFdeNMCcD2krMqv3m+GIMaHIuA/Lbyc9typSvS3uG9f+TYKAA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:14:36.688638Z","signed_message":"canonical_sha256_bytes"},"source_id":"2001.11938","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c00598c8c53096d492e6807f4cdbab4403a08b39ece24832425bdb4b0831842","sha256:ef4c1280e11c1f5d27cc8b6abb613ba449a9d707e217c9aaa494d74900b40031"],"state_sha256":"17bc7ea45cae6ef60dae5a3118ae5d2d05e9f8266a7c4eac97f25359e7a9051f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Edi8Bxwzq97qQWomETpJZY2kYnd6X/HKwrCeVDciH4+MLPDOZpUzKGqCOAQHc/asGP9KhA9zedEcLMBWoJOUCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T12:24:43.813742Z","bundle_sha256":"e419f115ca8040b7d4baa01a9d431f92410fc5308eba6d658747e0992fc2a843"}}