{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:KWYZU6I2GPGUPU3G4JZ25XTWBN","short_pith_number":"pith:KWYZU6I2","canonical_record":{"source":{"id":"2507.13321","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math-ph","submitted_at":"2025-07-17T17:41:53Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"8b12a0522e2d91e7ffaaa3bc772b30984b1c5f45677375f3d115e3b1f76cdb8b","abstract_canon_sha256":"73d3b6ae37d9b99e3dd1d2e346d05dccd144fb7a2b2551d992d444467f7fcf6a"},"schema_version":"1.0"},"canonical_sha256":"55b19a791a33cd47d366e273aede760b445cce8985c769b62179ea269cf79679","source":{"kind":"arxiv","id":"2507.13321","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.13321","created_at":"2026-07-05T11:50:21Z"},{"alias_kind":"arxiv_version","alias_value":"2507.13321v2","created_at":"2026-07-05T11:50:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.13321","created_at":"2026-07-05T11:50:21Z"},{"alias_kind":"pith_short_12","alias_value":"KWYZU6I2GPGU","created_at":"2026-07-05T11:50:21Z"},{"alias_kind":"pith_short_16","alias_value":"KWYZU6I2GPGUPU3G","created_at":"2026-07-05T11:50:21Z"},{"alias_kind":"pith_short_8","alias_value":"KWYZU6I2","created_at":"2026-07-05T11:50:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:KWYZU6I2GPGUPU3G4JZ25XTWBN","target":"record","payload":{"canonical_record":{"source":{"id":"2507.13321","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math-ph","submitted_at":"2025-07-17T17:41:53Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"8b12a0522e2d91e7ffaaa3bc772b30984b1c5f45677375f3d115e3b1f76cdb8b","abstract_canon_sha256":"73d3b6ae37d9b99e3dd1d2e346d05dccd144fb7a2b2551d992d444467f7fcf6a"},"schema_version":"1.0"},"canonical_sha256":"55b19a791a33cd47d366e273aede760b445cce8985c769b62179ea269cf79679","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:50:21.089784Z","signature_b64":"Vt2h3AE0f9bufGAAIROIa1w8HIvC5gbjDgvi8Qq7HBtTpdgQ0faL1FclVI9ghDSIBjJYHyWYTtMQTrY6k6k6AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55b19a791a33cd47d366e273aede760b445cce8985c769b62179ea269cf79679","last_reissued_at":"2026-07-05T11:50:21.089287Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:50:21.089287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.13321","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":"2026-07-05T11:50:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EFb9c15NY65pQ6+R+i8h1zEFVyCpGvV90jksPb1ed7IV3RjNHnDQueYSLs91KgEoD6r8ZPntKtKrXWTsRH6MDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T21:57:44.906344Z"},"content_sha256":"9730cc8c7415de6a174ff5d7ab05b7349ea3884996a234120f8de63ee4b6805d","schema_version":"1.0","event_id":"sha256:9730cc8c7415de6a174ff5d7ab05b7349ea3884996a234120f8de63ee4b6805d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:KWYZU6I2GPGUPU3G4JZ25XTWBN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Automorphic equivalence within gapped phases of infinitely extended fermion systems","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Lennart Becker, Marius Wesle, Stefan Teufel","submitted_at":"2025-07-17T17:41:53Z","abstract_excerpt":"We prove automorphic equivalence within gapped phases of infinitely extended lattice fermion systems (as well as spin systems) with super-polynomially decaying interactions. As a simple application, we prove a version of Goldstone's theorem for such systems: if an infinite volume interaction is invariant under a continuous symmetry, then any gapped ground state is also invariant under that symmetry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.13321","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/2507.13321/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":"2026-07-05T11:50:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rd7Lxp1h8vhyB/X/AV6QAnqL/n3sBY+zoOnGbWxY5QNQUmXXMyQcUfj5kBon/DbveXH6wOHdkD7hT7LmQyUDDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T21:57:44.906962Z"},"content_sha256":"0712e55f5e80ab5bde85a0ac63345f26a5e288814913ee080f79ec1ef7d36974","schema_version":"1.0","event_id":"sha256:0712e55f5e80ab5bde85a0ac63345f26a5e288814913ee080f79ec1ef7d36974"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KWYZU6I2GPGUPU3G4JZ25XTWBN/bundle.json","state_url":"https://pith.science/pith/KWYZU6I2GPGUPU3G4JZ25XTWBN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KWYZU6I2GPGUPU3G4JZ25XTWBN/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":"2026-08-19T21:57:44Z","links":{"resolver":"https://pith.science/pith/KWYZU6I2GPGUPU3G4JZ25XTWBN","bundle":"https://pith.science/pith/KWYZU6I2GPGUPU3G4JZ25XTWBN/bundle.json","state":"https://pith.science/pith/KWYZU6I2GPGUPU3G4JZ25XTWBN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KWYZU6I2GPGUPU3G4JZ25XTWBN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:KWYZU6I2GPGUPU3G4JZ25XTWBN","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":"73d3b6ae37d9b99e3dd1d2e346d05dccd144fb7a2b2551d992d444467f7fcf6a","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math-ph","submitted_at":"2025-07-17T17:41:53Z","title_canon_sha256":"8b12a0522e2d91e7ffaaa3bc772b30984b1c5f45677375f3d115e3b1f76cdb8b"},"schema_version":"1.0","source":{"id":"2507.13321","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.13321","created_at":"2026-07-05T11:50:21Z"},{"alias_kind":"arxiv_version","alias_value":"2507.13321v2","created_at":"2026-07-05T11:50:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.13321","created_at":"2026-07-05T11:50:21Z"},{"alias_kind":"pith_short_12","alias_value":"KWYZU6I2GPGU","created_at":"2026-07-05T11:50:21Z"},{"alias_kind":"pith_short_16","alias_value":"KWYZU6I2GPGUPU3G","created_at":"2026-07-05T11:50:21Z"},{"alias_kind":"pith_short_8","alias_value":"KWYZU6I2","created_at":"2026-07-05T11:50:21Z"}],"graph_snapshots":[{"event_id":"sha256:0712e55f5e80ab5bde85a0ac63345f26a5e288814913ee080f79ec1ef7d36974","target":"graph","created_at":"2026-07-05T11:50:21Z","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/2507.13321/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove automorphic equivalence within gapped phases of infinitely extended lattice fermion systems (as well as spin systems) with super-polynomially decaying interactions. As a simple application, we prove a version of Goldstone's theorem for such systems: if an infinite volume interaction is invariant under a continuous symmetry, then any gapped ground state is also invariant under that symmetry.","authors_text":"Lennart Becker, Marius Wesle, Stefan Teufel","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math-ph","submitted_at":"2025-07-17T17:41:53Z","title":"Automorphic equivalence within gapped phases of infinitely extended fermion systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.13321","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":"sha256:9730cc8c7415de6a174ff5d7ab05b7349ea3884996a234120f8de63ee4b6805d","target":"record","created_at":"2026-07-05T11:50:21Z","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":"73d3b6ae37d9b99e3dd1d2e346d05dccd144fb7a2b2551d992d444467f7fcf6a","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math-ph","submitted_at":"2025-07-17T17:41:53Z","title_canon_sha256":"8b12a0522e2d91e7ffaaa3bc772b30984b1c5f45677375f3d115e3b1f76cdb8b"},"schema_version":"1.0","source":{"id":"2507.13321","kind":"arxiv","version":2}},"canonical_sha256":"55b19a791a33cd47d366e273aede760b445cce8985c769b62179ea269cf79679","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55b19a791a33cd47d366e273aede760b445cce8985c769b62179ea269cf79679","first_computed_at":"2026-07-05T11:50:21.089287Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:50:21.089287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vt2h3AE0f9bufGAAIROIa1w8HIvC5gbjDgvi8Qq7HBtTpdgQ0faL1FclVI9ghDSIBjJYHyWYTtMQTrY6k6k6AA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:50:21.089784Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.13321","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9730cc8c7415de6a174ff5d7ab05b7349ea3884996a234120f8de63ee4b6805d","sha256:0712e55f5e80ab5bde85a0ac63345f26a5e288814913ee080f79ec1ef7d36974"],"state_sha256":"8a9eb52b18a3672e743ead2a7493f4e31326c1eb3ab04fba92ccb02ab2c944b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4GqLGg8HxofrJOXFFNi2Hq0G/cvTOFhz1ptIZVXmxpsFKxS3mVA8OjvfaJrjYZHmVPAAKK3CFipbo2noHfbwBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T21:57:44.913065Z","bundle_sha256":"d0bb58cab94be3e667c1b15d114427334ada0d65bcdd48ab60920e64131555a5"}}