{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:67DWQPBLLSKKGBWXZOR5GSILE7","short_pith_number":"pith:67DWQPBL","canonical_record":{"source":{"id":"math/0311108","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2003-11-07T12:01:31Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"71b8ba2603ed0d2153d9c513433c1c6e2d7b1acce4b8d7e60bfd116bce398e5a","abstract_canon_sha256":"d4b9d020c45a5db75f75fbb884c457b6b1d26f4b3a75f5ff8cd815cff82ad947"},"schema_version":"1.0"},"canonical_sha256":"f7c7683c2b5c94a306d7cba3d3490b27e39cc8cdc26112259baa1c5dad6d810c","source":{"kind":"arxiv","id":"math/0311108","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0311108","created_at":"2026-05-18T04:24:44Z"},{"alias_kind":"arxiv_version","alias_value":"math/0311108v3","created_at":"2026-05-18T04:24:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0311108","created_at":"2026-05-18T04:24:44Z"},{"alias_kind":"pith_short_12","alias_value":"67DWQPBLLSKK","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"67DWQPBLLSKKGBWX","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"67DWQPBL","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:67DWQPBLLSKKGBWXZOR5GSILE7","target":"record","payload":{"canonical_record":{"source":{"id":"math/0311108","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2003-11-07T12:01:31Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"71b8ba2603ed0d2153d9c513433c1c6e2d7b1acce4b8d7e60bfd116bce398e5a","abstract_canon_sha256":"d4b9d020c45a5db75f75fbb884c457b6b1d26f4b3a75f5ff8cd815cff82ad947"},"schema_version":"1.0"},"canonical_sha256":"f7c7683c2b5c94a306d7cba3d3490b27e39cc8cdc26112259baa1c5dad6d810c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:44.270113Z","signature_b64":"W9ToeUUraP4dWDQgNINCE1R1bQwWkkTHbFSA6wi9SXKgUT7OgT6wJNOe+BD+R6MjFVm6rKPjEWjD9vr24YrABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7c7683c2b5c94a306d7cba3d3490b27e39cc8cdc26112259baa1c5dad6d810c","last_reissued_at":"2026-05-18T04:24:44.269679Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:44.269679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0311108","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:24:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xU0QgOhoKaOF2qIPGXdhZTk3B3bmLMCxa4zuM86qXI3kRDmrH+6LX+1ANEIDSmVI4rCdX5zzScqlV3zla9qsCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T07:20:43.091091Z"},"content_sha256":"18cf40db55982f09d28cacd56df0d1a9a364dfe25cc1228517d3e7d8d793de6b","schema_version":"1.0","event_id":"sha256:18cf40db55982f09d28cacd56df0d1a9a364dfe25cc1228517d3e7d8d793de6b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:67DWQPBLLSKKGBWXZOR5GSILE7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Location of the 1-particle Branch of the Spectrum of the Disordered Stochastic Ising Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"M. Gianfelice, M. Isopi","submitted_at":"2003-11-07T12:01:31Z","abstract_excerpt":"We analyse the lower non trivial part of the spectrum of the generator of the Glauber dynamics, which we consider a positive operator, for a d-dimensional nearest neighbour Ising model with a bounded random potential. We prove conjecture 1 in a paper by Albeverio et al.(referred as [AMSZ]) that is, for sufficently large values of the temperature, the first band of the spectrum of the generator of the process coincides with a closed non random segment of the real line."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0311108","kind":"arxiv","version":3},"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":"2026-05-18T04:24:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jnUDYedlvR9OUf8GGQHtYWN1GdNrgYPUGyujiHTXcPkoEbFD25KrHSrYTlMENBrDNUV6PYWl1OFO1xD1R/MKDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T07:20:43.091752Z"},"content_sha256":"94e3c6be1b3a99940fcd1f7defb328f090b55f5bf149b8e744ce495e3e8aca10","schema_version":"1.0","event_id":"sha256:94e3c6be1b3a99940fcd1f7defb328f090b55f5bf149b8e744ce495e3e8aca10"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/67DWQPBLLSKKGBWXZOR5GSILE7/bundle.json","state_url":"https://pith.science/pith/67DWQPBLLSKKGBWXZOR5GSILE7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/67DWQPBLLSKKGBWXZOR5GSILE7/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":"2026-06-04T07:20:43Z","links":{"resolver":"https://pith.science/pith/67DWQPBLLSKKGBWXZOR5GSILE7","bundle":"https://pith.science/pith/67DWQPBLLSKKGBWXZOR5GSILE7/bundle.json","state":"https://pith.science/pith/67DWQPBLLSKKGBWXZOR5GSILE7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/67DWQPBLLSKKGBWXZOR5GSILE7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:67DWQPBLLSKKGBWXZOR5GSILE7","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":"d4b9d020c45a5db75f75fbb884c457b6b1d26f4b3a75f5ff8cd815cff82ad947","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2003-11-07T12:01:31Z","title_canon_sha256":"71b8ba2603ed0d2153d9c513433c1c6e2d7b1acce4b8d7e60bfd116bce398e5a"},"schema_version":"1.0","source":{"id":"math/0311108","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0311108","created_at":"2026-05-18T04:24:44Z"},{"alias_kind":"arxiv_version","alias_value":"math/0311108v3","created_at":"2026-05-18T04:24:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0311108","created_at":"2026-05-18T04:24:44Z"},{"alias_kind":"pith_short_12","alias_value":"67DWQPBLLSKK","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"67DWQPBLLSKKGBWX","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"67DWQPBL","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:94e3c6be1b3a99940fcd1f7defb328f090b55f5bf149b8e744ce495e3e8aca10","target":"graph","created_at":"2026-05-18T04:24:44Z","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 analyse the lower non trivial part of the spectrum of the generator of the Glauber dynamics, which we consider a positive operator, for a d-dimensional nearest neighbour Ising model with a bounded random potential. We prove conjecture 1 in a paper by Albeverio et al.(referred as [AMSZ]) that is, for sufficently large values of the temperature, the first band of the spectrum of the generator of the process coincides with a closed non random segment of the real line.","authors_text":"M. Gianfelice, M. Isopi","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2003-11-07T12:01:31Z","title":"On the Location of the 1-particle Branch of the Spectrum of the Disordered Stochastic Ising Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0311108","kind":"arxiv","version":3},"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":"sha256:18cf40db55982f09d28cacd56df0d1a9a364dfe25cc1228517d3e7d8d793de6b","target":"record","created_at":"2026-05-18T04:24:44Z","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":"d4b9d020c45a5db75f75fbb884c457b6b1d26f4b3a75f5ff8cd815cff82ad947","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2003-11-07T12:01:31Z","title_canon_sha256":"71b8ba2603ed0d2153d9c513433c1c6e2d7b1acce4b8d7e60bfd116bce398e5a"},"schema_version":"1.0","source":{"id":"math/0311108","kind":"arxiv","version":3}},"canonical_sha256":"f7c7683c2b5c94a306d7cba3d3490b27e39cc8cdc26112259baa1c5dad6d810c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7c7683c2b5c94a306d7cba3d3490b27e39cc8cdc26112259baa1c5dad6d810c","first_computed_at":"2026-05-18T04:24:44.269679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:44.269679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W9ToeUUraP4dWDQgNINCE1R1bQwWkkTHbFSA6wi9SXKgUT7OgT6wJNOe+BD+R6MjFVm6rKPjEWjD9vr24YrABw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:44.270113Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0311108","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18cf40db55982f09d28cacd56df0d1a9a364dfe25cc1228517d3e7d8d793de6b","sha256:94e3c6be1b3a99940fcd1f7defb328f090b55f5bf149b8e744ce495e3e8aca10"],"state_sha256":"2d286c48a7859a466cf933dabe38aa96b2fd637f23b5771e4a3107af19134bdb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ot8SWcvODYbnVvhRe27i6KBH7XgLLbt9NK8UlO5JtLjaKDSxCbygLMOuTF8g4LSvD/IFoZFnTDJ0jLl7C1OmDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T07:20:43.094760Z","bundle_sha256":"b5af1c37d9055321a683f63cda3f84fccfa7fb9fb7692661647de879f36c9349"}}