{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:HN4GOHNXVIXG3HI6LG3EZ3WJUQ","short_pith_number":"pith:HN4GOHNX","canonical_record":{"source":{"id":"2408.12600","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-08-22T17:59:38Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"0eb123e63400f15182ff3f7bea600e7e53486a334fb14246a7ca303cbc3c90dc","abstract_canon_sha256":"444baf90ecb433a7aa42e47bc6fc00ef668fd56f415c990c1f0ee474d00425f8"},"schema_version":"1.0"},"canonical_sha256":"3b78671db7aa2e6d9d1e59b64ceec9a430135b25ccd158c91264e638f2c26dc8","source":{"kind":"arxiv","id":"2408.12600","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.12600","created_at":"2026-07-05T08:58:17Z"},{"alias_kind":"arxiv_version","alias_value":"2408.12600v1","created_at":"2026-07-05T08:58:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.12600","created_at":"2026-07-05T08:58:17Z"},{"alias_kind":"pith_short_12","alias_value":"HN4GOHNXVIXG","created_at":"2026-07-05T08:58:17Z"},{"alias_kind":"pith_short_16","alias_value":"HN4GOHNXVIXG3HI6","created_at":"2026-07-05T08:58:17Z"},{"alias_kind":"pith_short_8","alias_value":"HN4GOHNX","created_at":"2026-07-05T08:58:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:HN4GOHNXVIXG3HI6LG3EZ3WJUQ","target":"record","payload":{"canonical_record":{"source":{"id":"2408.12600","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-08-22T17:59:38Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"0eb123e63400f15182ff3f7bea600e7e53486a334fb14246a7ca303cbc3c90dc","abstract_canon_sha256":"444baf90ecb433a7aa42e47bc6fc00ef668fd56f415c990c1f0ee474d00425f8"},"schema_version":"1.0"},"canonical_sha256":"3b78671db7aa2e6d9d1e59b64ceec9a430135b25ccd158c91264e638f2c26dc8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:58:17.263870Z","signature_b64":"xZ2cq4qYrDTsrZuBbUF/KUKxx3H/LaL6Y2RL1zZ+PkuInuWitq3EzAjyWVqAl3IBJSeVu8x/eqsQjuZ7WDDuCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b78671db7aa2e6d9d1e59b64ceec9a430135b25ccd158c91264e638f2c26dc8","last_reissued_at":"2026-07-05T08:58:17.263380Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:58:17.263380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2408.12600","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":"2026-07-05T08:58:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pvYOHSKlAI7n1//nfss9zbBXNoIUAnAhhnDBBQFFBp71+VJB87Kp/vJKsyuRteghJ+iG/spHrMJauEmJ+OwbBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T22:43:55.456670Z"},"content_sha256":"9c1235e954ff2c25eef580336c983f504e7b41869cec0f4bf9344108a7f6471f","schema_version":"1.0","event_id":"sha256:9c1235e954ff2c25eef580336c983f504e7b41869cec0f4bf9344108a7f6471f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:HN4GOHNXVIXG3HI6LG3EZ3WJUQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cornering Relative Symmetry Theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"hep-th","authors_text":"Ethan Torres, Jonathan J. Heckman, Max H\\\"ubner, Mirjam Cveti\\v{c}, Ron Donagi","submitted_at":"2024-08-22T17:59:38Z","abstract_excerpt":"The symmetry data of a $d$-dimensional quantum field theory (QFT) can often be captured in terms of a higher-dimensional symmetry topological field theory (SymTFT). In top down (i.e., stringy) realizations of this structure, the QFT in question is localized in a higher-dimensional bulk. In many cases of interest, however, the associated $(d+1)$-dimensional bulk is not fully gapped and one must instead consider a filtration of theories to reach a gapped bulk in $D = d+m$ dimensions. Overall, this leads us to a nested structure of relative symmetry theories which descend to coupled edge modes, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.12600","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/2408.12600/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":"2026-07-05T08:58:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6xXRy/eu8pSMoSmjw7ljrjLisOXd5aUeoCoyInC7ZT2/tBA2eriua9lgck222TS5BNGfQJ3WK5P6XHLoT+elAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T22:43:55.457184Z"},"content_sha256":"02b06af23bf5b1870dd481d932e9161277deeb885bcb59c37de059cb13ca52fd","schema_version":"1.0","event_id":"sha256:02b06af23bf5b1870dd481d932e9161277deeb885bcb59c37de059cb13ca52fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HN4GOHNXVIXG3HI6LG3EZ3WJUQ/bundle.json","state_url":"https://pith.science/pith/HN4GOHNXVIXG3HI6LG3EZ3WJUQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HN4GOHNXVIXG3HI6LG3EZ3WJUQ/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":"2026-08-20T22:43:55Z","links":{"resolver":"https://pith.science/pith/HN4GOHNXVIXG3HI6LG3EZ3WJUQ","bundle":"https://pith.science/pith/HN4GOHNXVIXG3HI6LG3EZ3WJUQ/bundle.json","state":"https://pith.science/pith/HN4GOHNXVIXG3HI6LG3EZ3WJUQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HN4GOHNXVIXG3HI6LG3EZ3WJUQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:HN4GOHNXVIXG3HI6LG3EZ3WJUQ","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":"444baf90ecb433a7aa42e47bc6fc00ef668fd56f415c990c1f0ee474d00425f8","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-08-22T17:59:38Z","title_canon_sha256":"0eb123e63400f15182ff3f7bea600e7e53486a334fb14246a7ca303cbc3c90dc"},"schema_version":"1.0","source":{"id":"2408.12600","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.12600","created_at":"2026-07-05T08:58:17Z"},{"alias_kind":"arxiv_version","alias_value":"2408.12600v1","created_at":"2026-07-05T08:58:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.12600","created_at":"2026-07-05T08:58:17Z"},{"alias_kind":"pith_short_12","alias_value":"HN4GOHNXVIXG","created_at":"2026-07-05T08:58:17Z"},{"alias_kind":"pith_short_16","alias_value":"HN4GOHNXVIXG3HI6","created_at":"2026-07-05T08:58:17Z"},{"alias_kind":"pith_short_8","alias_value":"HN4GOHNX","created_at":"2026-07-05T08:58:17Z"}],"graph_snapshots":[{"event_id":"sha256:02b06af23bf5b1870dd481d932e9161277deeb885bcb59c37de059cb13ca52fd","target":"graph","created_at":"2026-07-05T08:58:17Z","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/2408.12600/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The symmetry data of a $d$-dimensional quantum field theory (QFT) can often be captured in terms of a higher-dimensional symmetry topological field theory (SymTFT). In top down (i.e., stringy) realizations of this structure, the QFT in question is localized in a higher-dimensional bulk. In many cases of interest, however, the associated $(d+1)$-dimensional bulk is not fully gapped and one must instead consider a filtration of theories to reach a gapped bulk in $D = d+m$ dimensions. Overall, this leads us to a nested structure of relative symmetry theories which descend to coupled edge modes, w","authors_text":"Ethan Torres, Jonathan J. Heckman, Max H\\\"ubner, Mirjam Cveti\\v{c}, Ron Donagi","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-08-22T17:59:38Z","title":"Cornering Relative Symmetry Theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.12600","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":"sha256:9c1235e954ff2c25eef580336c983f504e7b41869cec0f4bf9344108a7f6471f","target":"record","created_at":"2026-07-05T08:58:17Z","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":"444baf90ecb433a7aa42e47bc6fc00ef668fd56f415c990c1f0ee474d00425f8","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2024-08-22T17:59:38Z","title_canon_sha256":"0eb123e63400f15182ff3f7bea600e7e53486a334fb14246a7ca303cbc3c90dc"},"schema_version":"1.0","source":{"id":"2408.12600","kind":"arxiv","version":1}},"canonical_sha256":"3b78671db7aa2e6d9d1e59b64ceec9a430135b25ccd158c91264e638f2c26dc8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b78671db7aa2e6d9d1e59b64ceec9a430135b25ccd158c91264e638f2c26dc8","first_computed_at":"2026-07-05T08:58:17.263380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:58:17.263380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xZ2cq4qYrDTsrZuBbUF/KUKxx3H/LaL6Y2RL1zZ+PkuInuWitq3EzAjyWVqAl3IBJSeVu8x/eqsQjuZ7WDDuCg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:58:17.263870Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.12600","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c1235e954ff2c25eef580336c983f504e7b41869cec0f4bf9344108a7f6471f","sha256:02b06af23bf5b1870dd481d932e9161277deeb885bcb59c37de059cb13ca52fd"],"state_sha256":"3a21aea4b5ca152d8d313535812f8f29077f3052956d1c38401ae9cc1445e67c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9fUxgwOZRSNxc7QjBO0bN+uFTBdmnOADmVguDF/t++J8liSSSvuOsFr5MRl3G4RrEKVGRlG9PB6U/SQgP5n8Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T22:43:55.461466Z","bundle_sha256":"1fbf7644bcf73b01d994079ea67747c8504bdb32aa3ddb249fa5b64d017d805f"}}