{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:6IOWIT6HDG7AOET67HODKMYQNR","short_pith_number":"pith:6IOWIT6H","canonical_record":{"source":{"id":"1111.6383","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-28T09:53:12Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"1afcc3859e81f5a94833dc7b41da87aff1e34666512e14af0e26af1872e493e1","abstract_canon_sha256":"f9a5f444d4ebb99b2357569e94bb802fc0121f1537ea769710676ea276167cb0"},"schema_version":"1.0"},"canonical_sha256":"f21d644fc719be07127ef9dc3533106c6659156b4aa16c5dc19e78109c7a933d","source":{"kind":"arxiv","id":"1111.6383","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.6383","created_at":"2026-05-18T03:11:22Z"},{"alias_kind":"arxiv_version","alias_value":"1111.6383v2","created_at":"2026-05-18T03:11:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6383","created_at":"2026-05-18T03:11:22Z"},{"alias_kind":"pith_short_12","alias_value":"6IOWIT6HDG7A","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6IOWIT6HDG7AOET6","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6IOWIT6H","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:6IOWIT6HDG7AOET67HODKMYQNR","target":"record","payload":{"canonical_record":{"source":{"id":"1111.6383","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-28T09:53:12Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"1afcc3859e81f5a94833dc7b41da87aff1e34666512e14af0e26af1872e493e1","abstract_canon_sha256":"f9a5f444d4ebb99b2357569e94bb802fc0121f1537ea769710676ea276167cb0"},"schema_version":"1.0"},"canonical_sha256":"f21d644fc719be07127ef9dc3533106c6659156b4aa16c5dc19e78109c7a933d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:22.211162Z","signature_b64":"HLr4wNkhUCe4oiPhyQfd+2IBEZf9wNXnv/5MVd5CMPh20bEykm5JaK1titWMVM3o7SRh7d3Ccmbt87eb4EmQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f21d644fc719be07127ef9dc3533106c6659156b4aa16c5dc19e78109c7a933d","last_reissued_at":"2026-05-18T03:11:22.210555Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:22.210555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.6383","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":"2026-05-18T03:11:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jRinPquLb1OctQ+/pNDB0subwdR6wgIFp2/aeQi2xxpWVpmU9cBeFZNwG4WmW4runfwpV/gGeN1eVmnPp7bsAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:52:30.453390Z"},"content_sha256":"13363d8a82723df5bd92085346109dcaf866f6f957f7cf7081e3e0f1226bacb0","schema_version":"1.0","event_id":"sha256:13363d8a82723df5bd92085346109dcaf866f6f957f7cf7081e3e0f1226bacb0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:6IOWIT6HDG7AOET67HODKMYQNR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Small perturbation of a disordered harmonic chain by a noise and an anharmonic potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"C\\'edric Bernardin, Fran\\c{c}ois Huveneers","submitted_at":"2011-11-28T09:53:12Z","abstract_excerpt":"We study the thermal properties of a pinned disordered harmonic chain weakly perturbed by a noise and an anharmonic potential. The noise is controlled by a parameter $\\lambda \\rightarrow 0$, and the anharmonicity by a parameter $\\lambda' \\le \\lambda$. Let $\\kappa$ be the conductivity of the chain, defined through the Green-Kubo formula. Under suitable hypotheses, we show that $\\kappa = \\mathcal O (\\lambda)$ and, in the absence of anharmonic potential, that $\\kappa \\sim \\lambda$. This is in sharp contrast with the ordered chain for which $\\kappa \\sim 1/\\lambda$, and so shows the persitence of l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6383","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":""},"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":"2026-05-18T03:11:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bf8PLSCnuD1vmewW1SluxfXU2hzIq3A83NfMvel2OH9IVhE6f1nqstWsRXGZ/zBfJjvEVlIECU8ldcc0UHyGCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:52:30.453764Z"},"content_sha256":"454dd0eb1ed2915e14d7e614992ea69f518aef2e5ec93bf4ae2d0b3de42e983b","schema_version":"1.0","event_id":"sha256:454dd0eb1ed2915e14d7e614992ea69f518aef2e5ec93bf4ae2d0b3de42e983b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6IOWIT6HDG7AOET67HODKMYQNR/bundle.json","state_url":"https://pith.science/pith/6IOWIT6HDG7AOET67HODKMYQNR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6IOWIT6HDG7AOET67HODKMYQNR/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":"2026-06-05T09:52:30Z","links":{"resolver":"https://pith.science/pith/6IOWIT6HDG7AOET67HODKMYQNR","bundle":"https://pith.science/pith/6IOWIT6HDG7AOET67HODKMYQNR/bundle.json","state":"https://pith.science/pith/6IOWIT6HDG7AOET67HODKMYQNR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6IOWIT6HDG7AOET67HODKMYQNR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6IOWIT6HDG7AOET67HODKMYQNR","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":"f9a5f444d4ebb99b2357569e94bb802fc0121f1537ea769710676ea276167cb0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-28T09:53:12Z","title_canon_sha256":"1afcc3859e81f5a94833dc7b41da87aff1e34666512e14af0e26af1872e493e1"},"schema_version":"1.0","source":{"id":"1111.6383","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.6383","created_at":"2026-05-18T03:11:22Z"},{"alias_kind":"arxiv_version","alias_value":"1111.6383v2","created_at":"2026-05-18T03:11:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6383","created_at":"2026-05-18T03:11:22Z"},{"alias_kind":"pith_short_12","alias_value":"6IOWIT6HDG7A","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6IOWIT6HDG7AOET6","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6IOWIT6H","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:454dd0eb1ed2915e14d7e614992ea69f518aef2e5ec93bf4ae2d0b3de42e983b","target":"graph","created_at":"2026-05-18T03:11:22Z","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 study the thermal properties of a pinned disordered harmonic chain weakly perturbed by a noise and an anharmonic potential. The noise is controlled by a parameter $\\lambda \\rightarrow 0$, and the anharmonicity by a parameter $\\lambda' \\le \\lambda$. Let $\\kappa$ be the conductivity of the chain, defined through the Green-Kubo formula. Under suitable hypotheses, we show that $\\kappa = \\mathcal O (\\lambda)$ and, in the absence of anharmonic potential, that $\\kappa \\sim \\lambda$. This is in sharp contrast with the ordered chain for which $\\kappa \\sim 1/\\lambda$, and so shows the persitence of l","authors_text":"C\\'edric Bernardin, Fran\\c{c}ois Huveneers","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-28T09:53:12Z","title":"Small perturbation of a disordered harmonic chain by a noise and an anharmonic potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6383","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":"sha256:13363d8a82723df5bd92085346109dcaf866f6f957f7cf7081e3e0f1226bacb0","target":"record","created_at":"2026-05-18T03:11:22Z","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":"f9a5f444d4ebb99b2357569e94bb802fc0121f1537ea769710676ea276167cb0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-28T09:53:12Z","title_canon_sha256":"1afcc3859e81f5a94833dc7b41da87aff1e34666512e14af0e26af1872e493e1"},"schema_version":"1.0","source":{"id":"1111.6383","kind":"arxiv","version":2}},"canonical_sha256":"f21d644fc719be07127ef9dc3533106c6659156b4aa16c5dc19e78109c7a933d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f21d644fc719be07127ef9dc3533106c6659156b4aa16c5dc19e78109c7a933d","first_computed_at":"2026-05-18T03:11:22.210555Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:22.210555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HLr4wNkhUCe4oiPhyQfd+2IBEZf9wNXnv/5MVd5CMPh20bEykm5JaK1titWMVM3o7SRh7d3Ccmbt87eb4EmQBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:22.211162Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.6383","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13363d8a82723df5bd92085346109dcaf866f6f957f7cf7081e3e0f1226bacb0","sha256:454dd0eb1ed2915e14d7e614992ea69f518aef2e5ec93bf4ae2d0b3de42e983b"],"state_sha256":"f7e0922012c70e657e2172acad0a6ce02f9dfdf42296a0ddb1e2092f8644e286"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5gZEa4vvvxgxrtJw4895dBHXzKD21cqNCU/bOfz1CgDw6LtZHwXWuuNrqMzgqOf+BOQHRZBkhyG+cz/x2s8wDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T09:52:30.455671Z","bundle_sha256":"d81fae243d0109fcfb653a4744a8f477487f2169946f8ae524ffe803eff4f612"}}