{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:B5I4ESXSER4HNBWKLMS3IGRONR","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":"52f9812a4e21ef275f2bb8f67bb10f8036ea1b7f91d95b4c819214df9719d85d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2010-03-16T20:57:46Z","title_canon_sha256":"11e62d7c8056f33ba37381744e670dd4e0224a0092f738d0a250b983a399777e"},"schema_version":"1.0","source":{"id":"1003.3248","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.3248","created_at":"2026-05-18T04:23:13Z"},{"alias_kind":"arxiv_version","alias_value":"1003.3248v2","created_at":"2026-05-18T04:23:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.3248","created_at":"2026-05-18T04:23:13Z"},{"alias_kind":"pith_short_12","alias_value":"B5I4ESXSER4H","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"B5I4ESXSER4HNBWK","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"B5I4ESXS","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:b8541382ef9343b6ffcd9e94f67673d92f81d9231bfe831edea31c17512ff561","target":"graph","created_at":"2026-05-18T04:23:13Z","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":"In this paper, we study the mechanics of statistically non-uniform two-phase elastic discrete structures. In particular, following the methodology proposed in (Luciano and Willis, Journal of the Mechanics and Physics of Solids 53, 1505-1522, 2005), energetic bounds and estimates of the Hashin-Shtrikman-Willis type are developed for discrete systems with a heterogeneity distribution quantified by second-order spatial statistics. As illustrated by three numerical case studies, the resulting expressions for the ensemble average of the potential energy are fully explicit, computationally feasible ","authors_text":"Jan Zeman, Marc G.D. Geers, Ron H.J. Peerlings","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2010-03-16T20:57:46Z","title":"Non-local energetics of random heterogeneous lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.3248","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:c6cd48167ace4a8cd55a70982ef4ca4e1fa90550593013326b37d6ec2544de2e","target":"record","created_at":"2026-05-18T04:23:13Z","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":"52f9812a4e21ef275f2bb8f67bb10f8036ea1b7f91d95b4c819214df9719d85d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2010-03-16T20:57:46Z","title_canon_sha256":"11e62d7c8056f33ba37381744e670dd4e0224a0092f738d0a250b983a399777e"},"schema_version":"1.0","source":{"id":"1003.3248","kind":"arxiv","version":2}},"canonical_sha256":"0f51c24af224787686ca5b25b41a2e6c4362e781ff8541163b51f2a16e8b3ff6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f51c24af224787686ca5b25b41a2e6c4362e781ff8541163b51f2a16e8b3ff6","first_computed_at":"2026-05-18T04:23:13.319614Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:13.319614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KdsPR0qLLvwls24+lwp6PrJyI4PuezSL3x8BEg90WNb2SbaNJv656FGR6AcnmT+8vEafZapHuHDzu2mOW8WqDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:13.320098Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.3248","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6cd48167ace4a8cd55a70982ef4ca4e1fa90550593013326b37d6ec2544de2e","sha256:b8541382ef9343b6ffcd9e94f67673d92f81d9231bfe831edea31c17512ff561"],"state_sha256":"30e3a5047ddd3299047a0141c02a33e1cbd57188794d11dbc5c4885ea767558a"}