{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:MGUG6JW4YEXXKMZT5JV6PZ7VJS","short_pith_number":"pith:MGUG6JW4","canonical_record":{"source":{"id":"1010.5360","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2010-10-26T11:15:54Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"3dbdfde8b230c0afa9ca592dec4c0a7f38e5f37c63c375e9bf17d68f00117216","abstract_canon_sha256":"9bbbdc4f9942bd3e89e557be0677ab9911ae966a8a423d38c33cf820e5462cf9"},"schema_version":"1.0"},"canonical_sha256":"61a86f26dcc12f753333ea6be7e7f54cb365c1e1bfd3d8bacca6238ae0c09262","source":{"kind":"arxiv","id":"1010.5360","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5360","created_at":"2026-05-18T02:04:58Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5360v1","created_at":"2026-05-18T02:04:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5360","created_at":"2026-05-18T02:04:58Z"},{"alias_kind":"pith_short_12","alias_value":"MGUG6JW4YEXX","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MGUG6JW4YEXXKMZT","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MGUG6JW4","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:MGUG6JW4YEXXKMZT5JV6PZ7VJS","target":"record","payload":{"canonical_record":{"source":{"id":"1010.5360","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2010-10-26T11:15:54Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"3dbdfde8b230c0afa9ca592dec4c0a7f38e5f37c63c375e9bf17d68f00117216","abstract_canon_sha256":"9bbbdc4f9942bd3e89e557be0677ab9911ae966a8a423d38c33cf820e5462cf9"},"schema_version":"1.0"},"canonical_sha256":"61a86f26dcc12f753333ea6be7e7f54cb365c1e1bfd3d8bacca6238ae0c09262","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:58.336994Z","signature_b64":"dvHnRSJxIjujhS/DirugY+FbEPVG81YLBWTN3R2elyWmQ2Zkw3ovxnSfnfspZAsD06DNpdTlrRo7wdDpAfrXAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61a86f26dcc12f753333ea6be7e7f54cb365c1e1bfd3d8bacca6238ae0c09262","last_reissued_at":"2026-05-18T02:04:58.336244Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:58.336244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.5360","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":"2026-05-18T02:04:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xyof75bxwpvXyb1UkK7BRpnQQOvlC3xaliqZtNm4iI9V2lYfD9rVh3KmTq+mn37ex8UWo/s+H5KnGfH1YA2mAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:07:21.528890Z"},"content_sha256":"e90eeec03432ab260ef7b4507d2300e5709a03265ad8292e44c78c709e66d909","schema_version":"1.0","event_id":"sha256:e90eeec03432ab260ef7b4507d2300e5709a03265ad8292e44c78c709e66d909"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:MGUG6JW4YEXXKMZT5JV6PZ7VJS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bifurcations in the optimal elastic foundation for a buckling column","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"physics.class-ph","authors_text":"Daniel Rayneau-Kirkhope, K. Ding, Robert Farr, Yong Mao","submitted_at":"2010-10-26T11:15:54Z","abstract_excerpt":"We investigate the buckling under compression of a slender beam with a distributed lateral elastic support, for which there is an associated cost. For a given cost, we study the optimal choice of support to protect against Euler buckling. We show that with only weak lateral support, the optimum distribution is a delta-function at the centre of the beam. When more support is allowed, we find numerically that the optimal distribution undergoes a series of bifurcations. We obtain analytical expressions for the buckling load around the first bifurcation point and corresponding expansions for the o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5360","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":"2026-05-18T02:04:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nUGLL4qa1alCVRkJyJ2bFB2aHF8+S87lqwSH0l2nzTy0Uj0lLdTvfQ8xI3fCDKQLa/pGA/6xnYLKJctjbrMpBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:07:21.529236Z"},"content_sha256":"06a0af7419abc67c195023acfdbf12c02254ec64ae517eccc68250bb4b1e2573","schema_version":"1.0","event_id":"sha256:06a0af7419abc67c195023acfdbf12c02254ec64ae517eccc68250bb4b1e2573"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MGUG6JW4YEXXKMZT5JV6PZ7VJS/bundle.json","state_url":"https://pith.science/pith/MGUG6JW4YEXXKMZT5JV6PZ7VJS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MGUG6JW4YEXXKMZT5JV6PZ7VJS/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":"2026-05-28T11:07:21Z","links":{"resolver":"https://pith.science/pith/MGUG6JW4YEXXKMZT5JV6PZ7VJS","bundle":"https://pith.science/pith/MGUG6JW4YEXXKMZT5JV6PZ7VJS/bundle.json","state":"https://pith.science/pith/MGUG6JW4YEXXKMZT5JV6PZ7VJS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MGUG6JW4YEXXKMZT5JV6PZ7VJS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:MGUG6JW4YEXXKMZT5JV6PZ7VJS","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":"9bbbdc4f9942bd3e89e557be0677ab9911ae966a8a423d38c33cf820e5462cf9","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2010-10-26T11:15:54Z","title_canon_sha256":"3dbdfde8b230c0afa9ca592dec4c0a7f38e5f37c63c375e9bf17d68f00117216"},"schema_version":"1.0","source":{"id":"1010.5360","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5360","created_at":"2026-05-18T02:04:58Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5360v1","created_at":"2026-05-18T02:04:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5360","created_at":"2026-05-18T02:04:58Z"},{"alias_kind":"pith_short_12","alias_value":"MGUG6JW4YEXX","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MGUG6JW4YEXXKMZT","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MGUG6JW4","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:06a0af7419abc67c195023acfdbf12c02254ec64ae517eccc68250bb4b1e2573","target":"graph","created_at":"2026-05-18T02:04:58Z","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 investigate the buckling under compression of a slender beam with a distributed lateral elastic support, for which there is an associated cost. For a given cost, we study the optimal choice of support to protect against Euler buckling. We show that with only weak lateral support, the optimum distribution is a delta-function at the centre of the beam. When more support is allowed, we find numerically that the optimal distribution undergoes a series of bifurcations. We obtain analytical expressions for the buckling load around the first bifurcation point and corresponding expansions for the o","authors_text":"Daniel Rayneau-Kirkhope, K. Ding, Robert Farr, Yong Mao","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2010-10-26T11:15:54Z","title":"Bifurcations in the optimal elastic foundation for a buckling column"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5360","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:e90eeec03432ab260ef7b4507d2300e5709a03265ad8292e44c78c709e66d909","target":"record","created_at":"2026-05-18T02:04:58Z","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":"9bbbdc4f9942bd3e89e557be0677ab9911ae966a8a423d38c33cf820e5462cf9","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2010-10-26T11:15:54Z","title_canon_sha256":"3dbdfde8b230c0afa9ca592dec4c0a7f38e5f37c63c375e9bf17d68f00117216"},"schema_version":"1.0","source":{"id":"1010.5360","kind":"arxiv","version":1}},"canonical_sha256":"61a86f26dcc12f753333ea6be7e7f54cb365c1e1bfd3d8bacca6238ae0c09262","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61a86f26dcc12f753333ea6be7e7f54cb365c1e1bfd3d8bacca6238ae0c09262","first_computed_at":"2026-05-18T02:04:58.336244Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:58.336244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dvHnRSJxIjujhS/DirugY+FbEPVG81YLBWTN3R2elyWmQ2Zkw3ovxnSfnfspZAsD06DNpdTlrRo7wdDpAfrXAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:58.336994Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.5360","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e90eeec03432ab260ef7b4507d2300e5709a03265ad8292e44c78c709e66d909","sha256:06a0af7419abc67c195023acfdbf12c02254ec64ae517eccc68250bb4b1e2573"],"state_sha256":"433b3a38c8366ad6f1b1a4f024a7ef6dc5f701c004695a3efa9844998a687f0b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wbZxMmP7DLpL+9HYh+AtLKtEnrQDcXIsJHVL5oIg1GWPklFg7iDdhd5G1/ZA0eH5CF1p44lzpT/DZsQJScKVCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T11:07:21.531241Z","bundle_sha256":"49ce46965e01a4543d1fe0cdcb461123c8ca89da4f354df072facbba4c8738a1"}}