{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:FQJLRM3VQL6UP36B7DXYNRAEF6","short_pith_number":"pith:FQJLRM3V","canonical_record":{"source":{"id":"2204.09117","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-04-19T20:29:53Z","cross_cats_sorted":[],"title_canon_sha256":"a4ad6283815f86682eacab17d012e8e8ac891d23d281a60d2fdfce4b3c310bdc","abstract_canon_sha256":"6087206b934db65e2f78183570cdbf0617cbb4aca4b8539631e0ab572f26d237"},"schema_version":"1.0"},"canonical_sha256":"2c12b8b37582fd47efc1f8ef86c4042f972a845aef745f1c9e787370615310e9","source":{"kind":"arxiv","id":"2204.09117","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.09117","created_at":"2026-07-05T04:16:21Z"},{"alias_kind":"arxiv_version","alias_value":"2204.09117v1","created_at":"2026-07-05T04:16:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.09117","created_at":"2026-07-05T04:16:21Z"},{"alias_kind":"pith_short_12","alias_value":"FQJLRM3VQL6U","created_at":"2026-07-05T04:16:21Z"},{"alias_kind":"pith_short_16","alias_value":"FQJLRM3VQL6UP36B","created_at":"2026-07-05T04:16:21Z"},{"alias_kind":"pith_short_8","alias_value":"FQJLRM3V","created_at":"2026-07-05T04:16:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:FQJLRM3VQL6UP36B7DXYNRAEF6","target":"record","payload":{"canonical_record":{"source":{"id":"2204.09117","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-04-19T20:29:53Z","cross_cats_sorted":[],"title_canon_sha256":"a4ad6283815f86682eacab17d012e8e8ac891d23d281a60d2fdfce4b3c310bdc","abstract_canon_sha256":"6087206b934db65e2f78183570cdbf0617cbb4aca4b8539631e0ab572f26d237"},"schema_version":"1.0"},"canonical_sha256":"2c12b8b37582fd47efc1f8ef86c4042f972a845aef745f1c9e787370615310e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:16:21.199232Z","signature_b64":"fGX6tgT91+KEK+oCwh2KD6SMfeRu2UKa6dW9ZQ9Hk3w21rpApAOpdCYTHjAV/4NB2wHGdx/XMwQjlCWGrrdkCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c12b8b37582fd47efc1f8ef86c4042f972a845aef745f1c9e787370615310e9","last_reissued_at":"2026-07-05T04:16:21.198831Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:16:21.198831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2204.09117","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":"2026-07-05T04:16:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M+BWKSYhOQThpMvTvN8aMX9GJxu5I60HOaH4D1okNfb5kOecg1ZdZvbcmzxhgvFrnDdSztAtHzmi5ys/yYrPBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T22:41:28.920352Z"},"content_sha256":"cf269bc82571ca1b26180928f6bff18c451cae377be8cf13758366cc8f1642c4","schema_version":"1.0","event_id":"sha256:cf269bc82571ca1b26180928f6bff18c451cae377be8cf13758366cc8f1642c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:FQJLRM3VQL6UP36B7DXYNRAEF6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An introduction to decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Eric Sharpe","submitted_at":"2022-04-19T20:29:53Z","abstract_excerpt":"We review work on `decomposition,' a property of two-dimensional theories with 1-form symmetries and, more generally, d-dimensional theories with (d-1)-form symmetries. Decomposition is the observation that such quantum field theories are equivalent to (`decompose into') disjoint unions of other QFTs, known in this context as \"universes.\" Examples include two-dimensional gauge theories and orbifolds with matter invariant under a subgroup of the gauge group. Decomposition explains and relates several physical properties of these theories -- for example, restrictions on allowed instantons arise "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.09117","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/2204.09117/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":"2026-07-05T04:16:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mI8b1HM/3AhdMF9+UbylO54oQx6iOGMAovzzRVYc8o0vNEZHs8uUCev0o0STw2PTSIOV4v/vH8EHeavUoVRrDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T22:41:28.920957Z"},"content_sha256":"30d638232c34b20c400d8324f3d53be428c40460cd84419c5129a57593913da8","schema_version":"1.0","event_id":"sha256:30d638232c34b20c400d8324f3d53be428c40460cd84419c5129a57593913da8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FQJLRM3VQL6UP36B7DXYNRAEF6/bundle.json","state_url":"https://pith.science/pith/FQJLRM3VQL6UP36B7DXYNRAEF6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FQJLRM3VQL6UP36B7DXYNRAEF6/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":"2026-08-10T22:41:28Z","links":{"resolver":"https://pith.science/pith/FQJLRM3VQL6UP36B7DXYNRAEF6","bundle":"https://pith.science/pith/FQJLRM3VQL6UP36B7DXYNRAEF6/bundle.json","state":"https://pith.science/pith/FQJLRM3VQL6UP36B7DXYNRAEF6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FQJLRM3VQL6UP36B7DXYNRAEF6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:FQJLRM3VQL6UP36B7DXYNRAEF6","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":"6087206b934db65e2f78183570cdbf0617cbb4aca4b8539631e0ab572f26d237","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-04-19T20:29:53Z","title_canon_sha256":"a4ad6283815f86682eacab17d012e8e8ac891d23d281a60d2fdfce4b3c310bdc"},"schema_version":"1.0","source":{"id":"2204.09117","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.09117","created_at":"2026-07-05T04:16:21Z"},{"alias_kind":"arxiv_version","alias_value":"2204.09117v1","created_at":"2026-07-05T04:16:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.09117","created_at":"2026-07-05T04:16:21Z"},{"alias_kind":"pith_short_12","alias_value":"FQJLRM3VQL6U","created_at":"2026-07-05T04:16:21Z"},{"alias_kind":"pith_short_16","alias_value":"FQJLRM3VQL6UP36B","created_at":"2026-07-05T04:16:21Z"},{"alias_kind":"pith_short_8","alias_value":"FQJLRM3V","created_at":"2026-07-05T04:16:21Z"}],"graph_snapshots":[{"event_id":"sha256:30d638232c34b20c400d8324f3d53be428c40460cd84419c5129a57593913da8","target":"graph","created_at":"2026-07-05T04:16:21Z","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/2204.09117/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We review work on `decomposition,' a property of two-dimensional theories with 1-form symmetries and, more generally, d-dimensional theories with (d-1)-form symmetries. Decomposition is the observation that such quantum field theories are equivalent to (`decompose into') disjoint unions of other QFTs, known in this context as \"universes.\" Examples include two-dimensional gauge theories and orbifolds with matter invariant under a subgroup of the gauge group. Decomposition explains and relates several physical properties of these theories -- for example, restrictions on allowed instantons arise ","authors_text":"Eric Sharpe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-04-19T20:29:53Z","title":"An introduction to decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.09117","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:cf269bc82571ca1b26180928f6bff18c451cae377be8cf13758366cc8f1642c4","target":"record","created_at":"2026-07-05T04:16:21Z","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":"6087206b934db65e2f78183570cdbf0617cbb4aca4b8539631e0ab572f26d237","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-04-19T20:29:53Z","title_canon_sha256":"a4ad6283815f86682eacab17d012e8e8ac891d23d281a60d2fdfce4b3c310bdc"},"schema_version":"1.0","source":{"id":"2204.09117","kind":"arxiv","version":1}},"canonical_sha256":"2c12b8b37582fd47efc1f8ef86c4042f972a845aef745f1c9e787370615310e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c12b8b37582fd47efc1f8ef86c4042f972a845aef745f1c9e787370615310e9","first_computed_at":"2026-07-05T04:16:21.198831Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:16:21.198831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fGX6tgT91+KEK+oCwh2KD6SMfeRu2UKa6dW9ZQ9Hk3w21rpApAOpdCYTHjAV/4NB2wHGdx/XMwQjlCWGrrdkCA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:16:21.199232Z","signed_message":"canonical_sha256_bytes"},"source_id":"2204.09117","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf269bc82571ca1b26180928f6bff18c451cae377be8cf13758366cc8f1642c4","sha256:30d638232c34b20c400d8324f3d53be428c40460cd84419c5129a57593913da8"],"state_sha256":"eaaaa08f44b67a814a8f21b851e17b28571e1c3775b62f4b463d90de9a3e9fd3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jID1q0IXkDsbG5EeSJ4k/E53Ip2dqih5r51T+z7MMqfZIkgsuO1Sww4CmcSlPW0QHLAVrmaZk9dKrib9VyuBDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T22:41:28.925469Z","bundle_sha256":"de1a3b53dec47dc6797313e80af863fc1819ee9907a28b19897b138180b8b2f0"}}