{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:3BTNMCLYA34RHZ3BDRYQVFLPDX","short_pith_number":"pith:3BTNMCLY","canonical_record":{"source":{"id":"2512.21687","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-12-25T14:23:15Z","cross_cats_sorted":["cond-mat.str-el","hep-ph","math-ph","math.MP","math.QA"],"title_canon_sha256":"e9631381088b5254689a77cb82096957d84c9993203dab52d55d275ba710c247","abstract_canon_sha256":"b7656cccd7d2d16a0bbb40b8302d675d15dd7d5d67b31fc47689a94422f351c8"},"schema_version":"1.0"},"canonical_sha256":"d866d6097806f913e7611c710a956f1de7cf340c2783964020ee36a9a2206711","source":{"kind":"arxiv","id":"2512.21687","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.21687","created_at":"2026-08-12T01:21:25Z"},{"alias_kind":"arxiv_version","alias_value":"2512.21687v4","created_at":"2026-08-12T01:21:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.21687","created_at":"2026-08-12T01:21:25Z"},{"alias_kind":"pith_short_12","alias_value":"3BTNMCLYA34R","created_at":"2026-08-12T01:21:25Z"},{"alias_kind":"pith_short_16","alias_value":"3BTNMCLYA34RHZ3B","created_at":"2026-08-12T01:21:25Z"},{"alias_kind":"pith_short_8","alias_value":"3BTNMCLY","created_at":"2026-08-12T01:21:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:3BTNMCLYA34RHZ3BDRYQVFLPDX","target":"record","payload":{"canonical_record":{"source":{"id":"2512.21687","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-12-25T14:23:15Z","cross_cats_sorted":["cond-mat.str-el","hep-ph","math-ph","math.MP","math.QA"],"title_canon_sha256":"e9631381088b5254689a77cb82096957d84c9993203dab52d55d275ba710c247","abstract_canon_sha256":"b7656cccd7d2d16a0bbb40b8302d675d15dd7d5d67b31fc47689a94422f351c8"},"schema_version":"1.0"},"canonical_sha256":"d866d6097806f913e7611c710a956f1de7cf340c2783964020ee36a9a2206711","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-12T01:21:25.112976Z","signature_b64":"fHYg3dlionWcV9moz19+kqTtQyPqHJ9yz9C3QrqtXRHh8zj/l6fk+iSMzNZigP1rimRdsD0nCitZI6dRjEVCAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d866d6097806f913e7611c710a956f1de7cf340c2783964020ee36a9a2206711","last_reissued_at":"2026-08-12T01:21:25.111276Z","signature_status":"signed_v1","first_computed_at":"2026-08-12T01:21:25.111276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2512.21687","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-12T01:21:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NSOiNuBaDf54YOw0TuuAZnYcsHlmy3V/J7sCQw8BDM3YWWMAniXHkMm+if7GX7wm4kzyE6OvN3wbl/wHpw9YAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T07:33:55.055622Z"},"content_sha256":"b18382b75594e9778825ab239c47b68b6173100693cdb4ce0680c6e558d1d001","schema_version":"1.0","event_id":"sha256:b18382b75594e9778825ab239c47b68b6173100693cdb4ce0680c6e558d1d001"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:3BTNMCLYA34RHZ3BDRYQVFLPDX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classifying fusion rules of anyons or SymTFTs: A general algebraic formula for domain wall problems and quantum phase transitions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","hep-ph","math-ph","math.MP","math.QA"],"primary_cat":"hep-th","authors_text":"Yoshiki Fukusumi","submitted_at":"2025-12-25T14:23:15Z","abstract_excerpt":"We propose a formula for the transformation law of anyons in topologically ordered phases or topological quantum field theories (TQFTs) through a gapped or symmetry-preserving domain wall. Our formalism is based on the ring homomorphism between the $\\mathbb{C}$-linear commutative fusion rings, also known as symmetry topological field theories (SymTFTs). The fundamental assumption in our formalism is the validity of the Verlinde formula, applicable to commutative fusion rings. By combining it with more specific data of the settings, our formula provides classifications of anyons compatible with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.21687","kind":"arxiv","version":4},"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/2512.21687/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":"2026-08-12T01:21:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O7BST98S8lJ0u5F6shYG53k3u8uXEvmnmIKGEF+eXomkcbtaZ81WdEFC/TldVEkP9px3Jt7RfIuqVn0kFl1OBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T07:33:55.056251Z"},"content_sha256":"282e8ddd0dbf3ef14bc1db3eeeaf95ed206c6354b89ea501c18ca8f485148d68","schema_version":"1.0","event_id":"sha256:282e8ddd0dbf3ef14bc1db3eeeaf95ed206c6354b89ea501c18ca8f485148d68"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3BTNMCLYA34RHZ3BDRYQVFLPDX/bundle.json","state_url":"https://pith.science/pith/3BTNMCLYA34RHZ3BDRYQVFLPDX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3BTNMCLYA34RHZ3BDRYQVFLPDX/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":"2026-08-15T07:33:55Z","links":{"resolver":"https://pith.science/pith/3BTNMCLYA34RHZ3BDRYQVFLPDX","bundle":"https://pith.science/pith/3BTNMCLYA34RHZ3BDRYQVFLPDX/bundle.json","state":"https://pith.science/pith/3BTNMCLYA34RHZ3BDRYQVFLPDX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3BTNMCLYA34RHZ3BDRYQVFLPDX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3BTNMCLYA34RHZ3BDRYQVFLPDX","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":"b7656cccd7d2d16a0bbb40b8302d675d15dd7d5d67b31fc47689a94422f351c8","cross_cats_sorted":["cond-mat.str-el","hep-ph","math-ph","math.MP","math.QA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-12-25T14:23:15Z","title_canon_sha256":"e9631381088b5254689a77cb82096957d84c9993203dab52d55d275ba710c247"},"schema_version":"1.0","source":{"id":"2512.21687","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.21687","created_at":"2026-08-12T01:21:25Z"},{"alias_kind":"arxiv_version","alias_value":"2512.21687v4","created_at":"2026-08-12T01:21:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.21687","created_at":"2026-08-12T01:21:25Z"},{"alias_kind":"pith_short_12","alias_value":"3BTNMCLYA34R","created_at":"2026-08-12T01:21:25Z"},{"alias_kind":"pith_short_16","alias_value":"3BTNMCLYA34RHZ3B","created_at":"2026-08-12T01:21:25Z"},{"alias_kind":"pith_short_8","alias_value":"3BTNMCLY","created_at":"2026-08-12T01:21:25Z"}],"graph_snapshots":[{"event_id":"sha256:282e8ddd0dbf3ef14bc1db3eeeaf95ed206c6354b89ea501c18ca8f485148d68","target":"graph","created_at":"2026-08-12T01:21:25Z","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/2512.21687/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a formula for the transformation law of anyons in topologically ordered phases or topological quantum field theories (TQFTs) through a gapped or symmetry-preserving domain wall. Our formalism is based on the ring homomorphism between the $\\mathbb{C}$-linear commutative fusion rings, also known as symmetry topological field theories (SymTFTs). The fundamental assumption in our formalism is the validity of the Verlinde formula, applicable to commutative fusion rings. By combining it with more specific data of the settings, our formula provides classifications of anyons compatible with","authors_text":"Yoshiki Fukusumi","cross_cats":["cond-mat.str-el","hep-ph","math-ph","math.MP","math.QA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-12-25T14:23:15Z","title":"Classifying fusion rules of anyons or SymTFTs: A general algebraic formula for domain wall problems and quantum phase transitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.21687","kind":"arxiv","version":4},"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:b18382b75594e9778825ab239c47b68b6173100693cdb4ce0680c6e558d1d001","target":"record","created_at":"2026-08-12T01:21:25Z","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":"b7656cccd7d2d16a0bbb40b8302d675d15dd7d5d67b31fc47689a94422f351c8","cross_cats_sorted":["cond-mat.str-el","hep-ph","math-ph","math.MP","math.QA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-12-25T14:23:15Z","title_canon_sha256":"e9631381088b5254689a77cb82096957d84c9993203dab52d55d275ba710c247"},"schema_version":"1.0","source":{"id":"2512.21687","kind":"arxiv","version":4}},"canonical_sha256":"d866d6097806f913e7611c710a956f1de7cf340c2783964020ee36a9a2206711","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d866d6097806f913e7611c710a956f1de7cf340c2783964020ee36a9a2206711","first_computed_at":"2026-08-12T01:21:25.111276Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-12T01:21:25.111276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fHYg3dlionWcV9moz19+kqTtQyPqHJ9yz9C3QrqtXRHh8zj/l6fk+iSMzNZigP1rimRdsD0nCitZI6dRjEVCAA==","signature_status":"signed_v1","signed_at":"2026-08-12T01:21:25.112976Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.21687","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b18382b75594e9778825ab239c47b68b6173100693cdb4ce0680c6e558d1d001","sha256:282e8ddd0dbf3ef14bc1db3eeeaf95ed206c6354b89ea501c18ca8f485148d68"],"state_sha256":"bc27d92fd9f820ffd41ca74471cc686ceab41505bf21f9871108de02f82abb4e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QE4lMnB+3/NtxoJXSq2el63UWkO10CKdgOTz0Cp6YIbQGLvkRd030R4aG8s+87ALtXjtYtNf4gkmSyrwuSrtAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T07:33:55.061119Z","bundle_sha256":"52d22cb31c633a987156582e12c1c0b0be0a33203c57e7137f4aa1d7014e9310"}}