{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:NBVPBQI5ARIIQ3OAVYCP5NP3XG","short_pith_number":"pith:NBVPBQI5","schema_version":"1.0","canonical_sha256":"686af0c11d0450886dc0ae04feb5fbb99d23bcc4e67ce433b40e4f5fc8fd86f5","source":{"kind":"arxiv","id":"1505.02919","version":1},"attestation_state":"computed","paper":{"title":"Asymptotic analysis of microscopic impenetrability constraints for atomistic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.OC"],"primary_cat":"math-ph","authors_text":"Andrea Braides, Maria Stella Gelli","submitted_at":"2015-05-12T09:14:02Z","abstract_excerpt":"In this paper we analyze a two-dimensional discrete model of nearest-neighbour Lennard-Jones interactions under the microscopical constraint that points on a lattice triangle maintain their order. This can be understood as a microscopical non-interpenetration constraint and amounts to the positiveness of the determinant of the gradient of the piecewise-affine interpolations of the discrete displacement. Under such a constraint we examine the continuum fracture energy deriving from a discrete-to-continuum analysis at a scaling where surface energy is preponderant. We give a lower bound by an an"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1505.02919","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-05-12T09:14:02Z","cross_cats_sorted":["math.AP","math.MP","math.OC"],"title_canon_sha256":"22bc4b273ae3a66c07f359e7e35507191fde89fe44216bb2b869719763511fe9","abstract_canon_sha256":"8a552eb20ce50a784cdadafc1c176550128e5ae8ade424e334240a365ee10c76"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:13.317857Z","signature_b64":"MisgF1oc5ueeiWxaAuKgU0IRp/eTVXYNacz8wkUWTef93M8QUGaioqLM4Z8fP3SPZR1Z9ZYuS1wdluf1oWt1Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"686af0c11d0450886dc0ae04feb5fbb99d23bcc4e67ce433b40e4f5fc8fd86f5","last_reissued_at":"2026-05-18T01:08:13.317117Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:13.317117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic analysis of microscopic impenetrability constraints for atomistic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.OC"],"primary_cat":"math-ph","authors_text":"Andrea Braides, Maria Stella Gelli","submitted_at":"2015-05-12T09:14:02Z","abstract_excerpt":"In this paper we analyze a two-dimensional discrete model of nearest-neighbour Lennard-Jones interactions under the microscopical constraint that points on a lattice triangle maintain their order. This can be understood as a microscopical non-interpenetration constraint and amounts to the positiveness of the determinant of the gradient of the piecewise-affine interpolations of the discrete displacement. Under such a constraint we examine the continuum fracture energy deriving from a discrete-to-continuum analysis at a scaling where surface energy is preponderant. We give a lower bound by an an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02919","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1505.02919","created_at":"2026-05-18T01:08:13.317220+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.02919v1","created_at":"2026-05-18T01:08:13.317220+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02919","created_at":"2026-05-18T01:08:13.317220+00:00"},{"alias_kind":"pith_short_12","alias_value":"NBVPBQI5ARII","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"NBVPBQI5ARIIQ3OA","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"NBVPBQI5","created_at":"2026-05-18T12:29:32.376354+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NBVPBQI5ARIIQ3OAVYCP5NP3XG","json":"https://pith.science/pith/NBVPBQI5ARIIQ3OAVYCP5NP3XG.json","graph_json":"https://pith.science/api/pith-number/NBVPBQI5ARIIQ3OAVYCP5NP3XG/graph.json","events_json":"https://pith.science/api/pith-number/NBVPBQI5ARIIQ3OAVYCP5NP3XG/events.json","paper":"https://pith.science/paper/NBVPBQI5"},"agent_actions":{"view_html":"https://pith.science/pith/NBVPBQI5ARIIQ3OAVYCP5NP3XG","download_json":"https://pith.science/pith/NBVPBQI5ARIIQ3OAVYCP5NP3XG.json","view_paper":"https://pith.science/paper/NBVPBQI5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.02919&json=true","fetch_graph":"https://pith.science/api/pith-number/NBVPBQI5ARIIQ3OAVYCP5NP3XG/graph.json","fetch_events":"https://pith.science/api/pith-number/NBVPBQI5ARIIQ3OAVYCP5NP3XG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NBVPBQI5ARIIQ3OAVYCP5NP3XG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NBVPBQI5ARIIQ3OAVYCP5NP3XG/action/storage_attestation","attest_author":"https://pith.science/pith/NBVPBQI5ARIIQ3OAVYCP5NP3XG/action/author_attestation","sign_citation":"https://pith.science/pith/NBVPBQI5ARIIQ3OAVYCP5NP3XG/action/citation_signature","submit_replication":"https://pith.science/pith/NBVPBQI5ARIIQ3OAVYCP5NP3XG/action/replication_record"}},"created_at":"2026-05-18T01:08:13.317220+00:00","updated_at":"2026-05-18T01:08:13.317220+00:00"}