{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NOFKGOAA2C6THNUVHDZ3YKCEAJ","short_pith_number":"pith:NOFKGOAA","canonical_record":{"source":{"id":"1509.07550","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-24T22:08:33Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"d4e43d4c0cfad6a797e5111e0ee871217bd5c6972e6f5087f00f775f8e282beb","abstract_canon_sha256":"3d6dc34c160faa419938a78d47fb420b17aa8360f31dc65b62cf9b44b85df5fa"},"schema_version":"1.0"},"canonical_sha256":"6b8aa33800d0bd33b69538f3bc28440273f07b2be97c124ee0b10ee95fae9676","source":{"kind":"arxiv","id":"1509.07550","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07550","created_at":"2026-05-18T01:07:58Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07550v1","created_at":"2026-05-18T01:07:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07550","created_at":"2026-05-18T01:07:58Z"},{"alias_kind":"pith_short_12","alias_value":"NOFKGOAA2C6T","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NOFKGOAA2C6THNUV","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NOFKGOAA","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NOFKGOAA2C6THNUVHDZ3YKCEAJ","target":"record","payload":{"canonical_record":{"source":{"id":"1509.07550","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-24T22:08:33Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"d4e43d4c0cfad6a797e5111e0ee871217bd5c6972e6f5087f00f775f8e282beb","abstract_canon_sha256":"3d6dc34c160faa419938a78d47fb420b17aa8360f31dc65b62cf9b44b85df5fa"},"schema_version":"1.0"},"canonical_sha256":"6b8aa33800d0bd33b69538f3bc28440273f07b2be97c124ee0b10ee95fae9676","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:58.456343Z","signature_b64":"3vTsnnTBqksvoRdUxMPqjHjOPhRyT7UaUgQ8cuEkez+LMrXEfEQebttd7nXWXubUPPbzzFWZAFzEJrwygZ1iCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b8aa33800d0bd33b69538f3bc28440273f07b2be97c124ee0b10ee95fae9676","last_reissued_at":"2026-05-18T01:07:58.455886Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:58.455886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.07550","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":"2026-05-18T01:07:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vB2+glWL7vIEHVT970DtiiJiJdBLXb3SDc1ddJNlZw6ZLdqcPrCeEB3awOsN/CAeBXZZdYTHpT6PvSViV1wqAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:48:23.598987Z"},"content_sha256":"ea4b832aa49a98aca2c46f482777957827995c247caacf3dc3e67701a2d49fd6","schema_version":"1.0","event_id":"sha256:ea4b832aa49a98aca2c46f482777957827995c247caacf3dc3e67701a2d49fd6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NOFKGOAA2C6THNUVHDZ3YKCEAJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral Gap and Edge Excitations of $d$-dimensional PVBS models on half-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Amanda Young, Bruno Nachtergaele, Michael Bishop","submitted_at":"2015-09-24T22:08:33Z","abstract_excerpt":"We analyze a class of quantum spin models defined on half-spaces in the $d$-dimensional hypercubic lattice bounded by a hyperplane with inward unit normal vector $m\\in\\mathbb{R}^d$. The family of models was previously introduced as the single species Product Vacua with Boundary States (PVBS) model, which is a spin-$1/2$ model with a XXZ-type nearest neighbor interactions depending on parameters $\\lambda_j\\in (0,\\infty)$, one for each coordinate direction. For any given values of the parameters, we prove an upper bound for the spectral gap above the unique ground state of these models, which va"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07550","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":"2026-05-18T01:07:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g8PO2dvoVndpAQtDFbyheVWOrxl52tQPBK5R68Yshg/EoMUguqhFAKhkeANWR80V38w2ommS2/EWDCjwaL+DBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:48:23.599701Z"},"content_sha256":"5e8fc0f10d81fe32c1b4bba9fd906222a87e6b1c9217ce79dca1a17ab23da95e","schema_version":"1.0","event_id":"sha256:5e8fc0f10d81fe32c1b4bba9fd906222a87e6b1c9217ce79dca1a17ab23da95e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NOFKGOAA2C6THNUVHDZ3YKCEAJ/bundle.json","state_url":"https://pith.science/pith/NOFKGOAA2C6THNUVHDZ3YKCEAJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NOFKGOAA2C6THNUVHDZ3YKCEAJ/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":"2026-05-27T19:48:23Z","links":{"resolver":"https://pith.science/pith/NOFKGOAA2C6THNUVHDZ3YKCEAJ","bundle":"https://pith.science/pith/NOFKGOAA2C6THNUVHDZ3YKCEAJ/bundle.json","state":"https://pith.science/pith/NOFKGOAA2C6THNUVHDZ3YKCEAJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NOFKGOAA2C6THNUVHDZ3YKCEAJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NOFKGOAA2C6THNUVHDZ3YKCEAJ","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":"3d6dc34c160faa419938a78d47fb420b17aa8360f31dc65b62cf9b44b85df5fa","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-24T22:08:33Z","title_canon_sha256":"d4e43d4c0cfad6a797e5111e0ee871217bd5c6972e6f5087f00f775f8e282beb"},"schema_version":"1.0","source":{"id":"1509.07550","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07550","created_at":"2026-05-18T01:07:58Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07550v1","created_at":"2026-05-18T01:07:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07550","created_at":"2026-05-18T01:07:58Z"},{"alias_kind":"pith_short_12","alias_value":"NOFKGOAA2C6T","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NOFKGOAA2C6THNUV","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NOFKGOAA","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:5e8fc0f10d81fe32c1b4bba9fd906222a87e6b1c9217ce79dca1a17ab23da95e","target":"graph","created_at":"2026-05-18T01:07:58Z","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 analyze a class of quantum spin models defined on half-spaces in the $d$-dimensional hypercubic lattice bounded by a hyperplane with inward unit normal vector $m\\in\\mathbb{R}^d$. The family of models was previously introduced as the single species Product Vacua with Boundary States (PVBS) model, which is a spin-$1/2$ model with a XXZ-type nearest neighbor interactions depending on parameters $\\lambda_j\\in (0,\\infty)$, one for each coordinate direction. For any given values of the parameters, we prove an upper bound for the spectral gap above the unique ground state of these models, which va","authors_text":"Amanda Young, Bruno Nachtergaele, Michael Bishop","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-24T22:08:33Z","title":"Spectral Gap and Edge Excitations of $d$-dimensional PVBS models on half-spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07550","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:ea4b832aa49a98aca2c46f482777957827995c247caacf3dc3e67701a2d49fd6","target":"record","created_at":"2026-05-18T01:07:58Z","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":"3d6dc34c160faa419938a78d47fb420b17aa8360f31dc65b62cf9b44b85df5fa","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-24T22:08:33Z","title_canon_sha256":"d4e43d4c0cfad6a797e5111e0ee871217bd5c6972e6f5087f00f775f8e282beb"},"schema_version":"1.0","source":{"id":"1509.07550","kind":"arxiv","version":1}},"canonical_sha256":"6b8aa33800d0bd33b69538f3bc28440273f07b2be97c124ee0b10ee95fae9676","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b8aa33800d0bd33b69538f3bc28440273f07b2be97c124ee0b10ee95fae9676","first_computed_at":"2026-05-18T01:07:58.455886Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:58.455886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3vTsnnTBqksvoRdUxMPqjHjOPhRyT7UaUgQ8cuEkez+LMrXEfEQebttd7nXWXubUPPbzzFWZAFzEJrwygZ1iCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:58.456343Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.07550","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea4b832aa49a98aca2c46f482777957827995c247caacf3dc3e67701a2d49fd6","sha256:5e8fc0f10d81fe32c1b4bba9fd906222a87e6b1c9217ce79dca1a17ab23da95e"],"state_sha256":"604e185a2e28925ccdb8f679c9558de129a70476d0cbf7c8670e285b8cd0f0e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QgGbj89/1sMsDydaBlPGGwGg5Q0h2YstcPGk5vB2/i/eEmr6/WXvZLGFlHv/+nNUWthKVkJTq/fe8wg6a5jOCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T19:48:23.603034Z","bundle_sha256":"19eed7a9799eefaeb0749ed8f309d2a9ff30ff8e5dd19bba33a98659939bd399"}}