{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:Y72TLQJUKMR6BFITTTTOZVQ556","short_pith_number":"pith:Y72TLQJU","canonical_record":{"source":{"id":"1208.5727","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-08-28T17:59:27Z","cross_cats_sorted":["physics.atm-clus"],"title_canon_sha256":"8e44d7fa318dc4837c49bfa78464478bc8132ed7fba06c45dd1f129813ca9be2","abstract_canon_sha256":"a3987ba81d9e0da93d292fa40aa3ba72f860441ee59fda568e40d835e928b61d"},"schema_version":"1.0"},"canonical_sha256":"c7f535c1345323e095139ce6ecd61def9797787fcb946a5f98b8204cb5f4b932","source":{"kind":"arxiv","id":"1208.5727","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.5727","created_at":"2026-05-18T03:46:57Z"},{"alias_kind":"arxiv_version","alias_value":"1208.5727v1","created_at":"2026-05-18T03:46:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5727","created_at":"2026-05-18T03:46:57Z"},{"alias_kind":"pith_short_12","alias_value":"Y72TLQJUKMR6","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"Y72TLQJUKMR6BFIT","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"Y72TLQJU","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:Y72TLQJUKMR6BFITTTTOZVQ556","target":"record","payload":{"canonical_record":{"source":{"id":"1208.5727","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-08-28T17:59:27Z","cross_cats_sorted":["physics.atm-clus"],"title_canon_sha256":"8e44d7fa318dc4837c49bfa78464478bc8132ed7fba06c45dd1f129813ca9be2","abstract_canon_sha256":"a3987ba81d9e0da93d292fa40aa3ba72f860441ee59fda568e40d835e928b61d"},"schema_version":"1.0"},"canonical_sha256":"c7f535c1345323e095139ce6ecd61def9797787fcb946a5f98b8204cb5f4b932","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:57.936748Z","signature_b64":"3NrywRnMy8Pqy6UBqfZ6N9cOe3wctfsPoGRcSxE1KC96c1uKq9PIse8FBCt5G85gm6TnArLxamXb62AuGKqzBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7f535c1345323e095139ce6ecd61def9797787fcb946a5f98b8204cb5f4b932","last_reissued_at":"2026-05-18T03:46:57.936038Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:57.936038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.5727","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":"2026-05-18T03:46:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lx/8ZbhuLJAnFWdCV9iMj30TEo8G5GMCH5OCy59VYz7V5c9DtcE1Te8cKJ+Xz8WG7IBe/4hKSadQ1BK4N6y5BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:26:20.484951Z"},"content_sha256":"d5b9ca73ccdfeefc0b9efc6cb3d6f9c4f413e4afd01bbfd38ee3886c7c63b10d","schema_version":"1.0","event_id":"sha256:d5b9ca73ccdfeefc0b9efc6cb3d6f9c4f413e4afd01bbfd38ee3886c7c63b10d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:Y72TLQJUKMR6BFITTTTOZVQ556","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mechanics of dislocation pile-ups: A unification of scaling regimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.atm-clus"],"primary_cat":"math.OC","authors_text":"Lucia Scardia, Marc G.D. Geers, Mark A. Peletier, Ron H.J. Peerlings","submitted_at":"2012-08-28T17:59:27Z","abstract_excerpt":"This paper unravels the problem of an idealised pile-up of n infinite, equi-spaced walls of edge dislocations at equilibrium. We define a dimensionless parameter that depends on the geometric, constitutive and loading parameters of the problem, and we identify five different scaling regimes corresponding to different values of that parameter for large n. For each of the cases we perform a rigorous micro-to-meso upscaling, and we obtain five expressions for the mesoscopic (continuum) internal stress. We recover some expressions for the internal stress that are already in use in the mechanical c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5727","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":"2026-05-18T03:46:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AidHi69XFZjvcuGVzuk4o/sNax2eV1+zcoUkOcd9iENVg6PBgd95Ai1X3fKCF/2imXbsW/9JF+AweKDNSNuOBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:26:20.485725Z"},"content_sha256":"f6fdd083fafce593889956bf08e971d6d7fd16a673435f1e7d946e013bda8980","schema_version":"1.0","event_id":"sha256:f6fdd083fafce593889956bf08e971d6d7fd16a673435f1e7d946e013bda8980"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y72TLQJUKMR6BFITTTTOZVQ556/bundle.json","state_url":"https://pith.science/pith/Y72TLQJUKMR6BFITTTTOZVQ556/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y72TLQJUKMR6BFITTTTOZVQ556/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":"2026-05-31T16:26:20Z","links":{"resolver":"https://pith.science/pith/Y72TLQJUKMR6BFITTTTOZVQ556","bundle":"https://pith.science/pith/Y72TLQJUKMR6BFITTTTOZVQ556/bundle.json","state":"https://pith.science/pith/Y72TLQJUKMR6BFITTTTOZVQ556/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y72TLQJUKMR6BFITTTTOZVQ556/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Y72TLQJUKMR6BFITTTTOZVQ556","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":"a3987ba81d9e0da93d292fa40aa3ba72f860441ee59fda568e40d835e928b61d","cross_cats_sorted":["physics.atm-clus"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-08-28T17:59:27Z","title_canon_sha256":"8e44d7fa318dc4837c49bfa78464478bc8132ed7fba06c45dd1f129813ca9be2"},"schema_version":"1.0","source":{"id":"1208.5727","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.5727","created_at":"2026-05-18T03:46:57Z"},{"alias_kind":"arxiv_version","alias_value":"1208.5727v1","created_at":"2026-05-18T03:46:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5727","created_at":"2026-05-18T03:46:57Z"},{"alias_kind":"pith_short_12","alias_value":"Y72TLQJUKMR6","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"Y72TLQJUKMR6BFIT","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"Y72TLQJU","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:f6fdd083fafce593889956bf08e971d6d7fd16a673435f1e7d946e013bda8980","target":"graph","created_at":"2026-05-18T03:46:57Z","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":"This paper unravels the problem of an idealised pile-up of n infinite, equi-spaced walls of edge dislocations at equilibrium. We define a dimensionless parameter that depends on the geometric, constitutive and loading parameters of the problem, and we identify five different scaling regimes corresponding to different values of that parameter for large n. For each of the cases we perform a rigorous micro-to-meso upscaling, and we obtain five expressions for the mesoscopic (continuum) internal stress. We recover some expressions for the internal stress that are already in use in the mechanical c","authors_text":"Lucia Scardia, Marc G.D. Geers, Mark A. Peletier, Ron H.J. Peerlings","cross_cats":["physics.atm-clus"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-08-28T17:59:27Z","title":"Mechanics of dislocation pile-ups: A unification of scaling regimes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5727","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:d5b9ca73ccdfeefc0b9efc6cb3d6f9c4f413e4afd01bbfd38ee3886c7c63b10d","target":"record","created_at":"2026-05-18T03:46:57Z","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":"a3987ba81d9e0da93d292fa40aa3ba72f860441ee59fda568e40d835e928b61d","cross_cats_sorted":["physics.atm-clus"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-08-28T17:59:27Z","title_canon_sha256":"8e44d7fa318dc4837c49bfa78464478bc8132ed7fba06c45dd1f129813ca9be2"},"schema_version":"1.0","source":{"id":"1208.5727","kind":"arxiv","version":1}},"canonical_sha256":"c7f535c1345323e095139ce6ecd61def9797787fcb946a5f98b8204cb5f4b932","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7f535c1345323e095139ce6ecd61def9797787fcb946a5f98b8204cb5f4b932","first_computed_at":"2026-05-18T03:46:57.936038Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:57.936038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3NrywRnMy8Pqy6UBqfZ6N9cOe3wctfsPoGRcSxE1KC96c1uKq9PIse8FBCt5G85gm6TnArLxamXb62AuGKqzBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:57.936748Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.5727","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5b9ca73ccdfeefc0b9efc6cb3d6f9c4f413e4afd01bbfd38ee3886c7c63b10d","sha256:f6fdd083fafce593889956bf08e971d6d7fd16a673435f1e7d946e013bda8980"],"state_sha256":"1359b52bfad0015ecb588f6e18b6016c50de362dc094e5b1c0f4ac928286c3d0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ka7Ab99wAbjYxjSJ9wPP5HW7mDKsnsPbATNpA0U7zoDE+aP+/z1Ixf5oahDt1rsJGAzMvoIboglq7ZTudNH1BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T16:26:20.489888Z","bundle_sha256":"c9d2e2d319bfd9fd01dab8c62a747a227b9de0d7c433524dabb91045b0812344"}}