{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1994:KJ5KQQGFAKDONJPUOA6PHXWATO","short_pith_number":"pith:KJ5KQQGF","canonical_record":{"source":{"id":"cond-mat/9410110","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat","submitted_at":"1994-10-29T19:12:09Z","cross_cats_sorted":[],"title_canon_sha256":"10df578704ef532351d6dfc010f8f7e358c51b9d151960a944e4d1654f16087f","abstract_canon_sha256":"988d106b04c980c5b431e904350b20c9b2da95fa4b658cd05532023ba8d20f69"},"schema_version":"1.0"},"canonical_sha256":"527aa840c50286e6a5f4703cf3dec09b91e75679e5edaa193beff5cae02fcd06","source":{"kind":"arxiv","id":"cond-mat/9410110","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9410110","created_at":"2026-05-18T01:39:35Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9410110v1","created_at":"2026-05-18T01:39:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9410110","created_at":"2026-05-18T01:39:35Z"},{"alias_kind":"pith_short_12","alias_value":"KJ5KQQGFAKDO","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"KJ5KQQGFAKDONJPU","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"KJ5KQQGF","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1994:KJ5KQQGFAKDONJPUOA6PHXWATO","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/9410110","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat","submitted_at":"1994-10-29T19:12:09Z","cross_cats_sorted":[],"title_canon_sha256":"10df578704ef532351d6dfc010f8f7e358c51b9d151960a944e4d1654f16087f","abstract_canon_sha256":"988d106b04c980c5b431e904350b20c9b2da95fa4b658cd05532023ba8d20f69"},"schema_version":"1.0"},"canonical_sha256":"527aa840c50286e6a5f4703cf3dec09b91e75679e5edaa193beff5cae02fcd06","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:35.444768Z","signature_b64":"Ha+R4XY20Yj5Ja4iaMlTbRHkEuQ+mgp9jJidmw0eUMAS6TZAghBl6Mfc1NJhb6wOgJEWKKsWxL6jFY+2seWsDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"527aa840c50286e6a5f4703cf3dec09b91e75679e5edaa193beff5cae02fcd06","last_reissued_at":"2026-05-18T01:39:35.444119Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:35.444119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/9410110","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":"2026-05-18T01:39:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lQmC6zJy1X2DaUD/s35xONhO1N2TWy+WxiGj8quI1UB4bYf8VtYotq2+nRdG2+IR64bzf58g6uvuNldYkLtzCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:57:42.986820Z"},"content_sha256":"37ee4511887cb3bab1fe71cab917f6e6f10bd604b2dd9d535d056031830a9c47","schema_version":"1.0","event_id":"sha256:37ee4511887cb3bab1fe71cab917f6e6f10bd604b2dd9d535d056031830a9c47"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1994:KJ5KQQGFAKDONJPUOA6PHXWATO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The spectral gap for some spin chains with discrete symmetry breaking","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat","authors_text":"Bruno Nachtergaele","submitted_at":"1994-10-29T19:12:09Z","abstract_excerpt":"We prove that for any finite set of generalized valence bond solid (GVBS) states of a quantum spin chain there exists a translation invariant finite-range Hamiltonian for which this set is the set of ground states. This result implies that there are GVBS models with arbitrary broken discrete symmetries that are described as combinations of lattice translations, lattice reflections, and local unitary or anti-unitary transformations. We also show that all GVBS models that satisfy some natural conditions have a spectral gap. The existence of a spectral gap is obtained by applying a simple and qui"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9410110","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":""},"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":"2026-05-18T01:39:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c+zq/y3v+Ri3xRNZ8zJJc8fiti+d4+y1IGsD6+yQVC5vE/FMYQVaLvjwJ1heseV86xkR8/sJ3Z206bz6CojLDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:57:42.987168Z"},"content_sha256":"445326b5d8b0f3a069b72d636ebfd1d193ec946bdbe7f5f827ab894b024575ae","schema_version":"1.0","event_id":"sha256:445326b5d8b0f3a069b72d636ebfd1d193ec946bdbe7f5f827ab894b024575ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KJ5KQQGFAKDONJPUOA6PHXWATO/bundle.json","state_url":"https://pith.science/pith/KJ5KQQGFAKDONJPUOA6PHXWATO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KJ5KQQGFAKDONJPUOA6PHXWATO/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":"2026-05-28T00:57:42Z","links":{"resolver":"https://pith.science/pith/KJ5KQQGFAKDONJPUOA6PHXWATO","bundle":"https://pith.science/pith/KJ5KQQGFAKDONJPUOA6PHXWATO/bundle.json","state":"https://pith.science/pith/KJ5KQQGFAKDONJPUOA6PHXWATO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KJ5KQQGFAKDONJPUOA6PHXWATO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1994:KJ5KQQGFAKDONJPUOA6PHXWATO","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":"988d106b04c980c5b431e904350b20c9b2da95fa4b658cd05532023ba8d20f69","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat","submitted_at":"1994-10-29T19:12:09Z","title_canon_sha256":"10df578704ef532351d6dfc010f8f7e358c51b9d151960a944e4d1654f16087f"},"schema_version":"1.0","source":{"id":"cond-mat/9410110","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9410110","created_at":"2026-05-18T01:39:35Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9410110v1","created_at":"2026-05-18T01:39:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9410110","created_at":"2026-05-18T01:39:35Z"},{"alias_kind":"pith_short_12","alias_value":"KJ5KQQGFAKDO","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"KJ5KQQGFAKDONJPU","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"KJ5KQQGF","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:445326b5d8b0f3a069b72d636ebfd1d193ec946bdbe7f5f827ab894b024575ae","target":"graph","created_at":"2026-05-18T01:39:35Z","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"},"paper":{"abstract_excerpt":"We prove that for any finite set of generalized valence bond solid (GVBS) states of a quantum spin chain there exists a translation invariant finite-range Hamiltonian for which this set is the set of ground states. This result implies that there are GVBS models with arbitrary broken discrete symmetries that are described as combinations of lattice translations, lattice reflections, and local unitary or anti-unitary transformations. We also show that all GVBS models that satisfy some natural conditions have a spectral gap. The existence of a spectral gap is obtained by applying a simple and qui","authors_text":"Bruno Nachtergaele","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat","submitted_at":"1994-10-29T19:12:09Z","title":"The spectral gap for some spin chains with discrete symmetry breaking"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9410110","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":"sha256:37ee4511887cb3bab1fe71cab917f6e6f10bd604b2dd9d535d056031830a9c47","target":"record","created_at":"2026-05-18T01:39:35Z","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":"988d106b04c980c5b431e904350b20c9b2da95fa4b658cd05532023ba8d20f69","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat","submitted_at":"1994-10-29T19:12:09Z","title_canon_sha256":"10df578704ef532351d6dfc010f8f7e358c51b9d151960a944e4d1654f16087f"},"schema_version":"1.0","source":{"id":"cond-mat/9410110","kind":"arxiv","version":1}},"canonical_sha256":"527aa840c50286e6a5f4703cf3dec09b91e75679e5edaa193beff5cae02fcd06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"527aa840c50286e6a5f4703cf3dec09b91e75679e5edaa193beff5cae02fcd06","first_computed_at":"2026-05-18T01:39:35.444119Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:35.444119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ha+R4XY20Yj5Ja4iaMlTbRHkEuQ+mgp9jJidmw0eUMAS6TZAghBl6Mfc1NJhb6wOgJEWKKsWxL6jFY+2seWsDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:35.444768Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/9410110","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37ee4511887cb3bab1fe71cab917f6e6f10bd604b2dd9d535d056031830a9c47","sha256:445326b5d8b0f3a069b72d636ebfd1d193ec946bdbe7f5f827ab894b024575ae"],"state_sha256":"cb531bc89c9521f86c6e8abdfa537477593c5f23c4b2957c403f7964597bd00e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MeioaYQe+vfokeSZ03PtMD3WZl31kR0i0B5NLVcPwXhGfWMX1IM1JyId06RipenJDqPpDn2FdioVW6DfEcqmDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T00:57:42.989311Z","bundle_sha256":"03ce30bc73fc7a8c9767f3c4ebb9f6bece61d7d4d65bfd2505e6b9506e95b0b5"}}