{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:M6KUXXV36HTN3LH53A5RKNTHIG","short_pith_number":"pith:M6KUXXV3","canonical_record":{"source":{"id":"1612.05620","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-16T20:23:00Z","cross_cats_sorted":[],"title_canon_sha256":"5c528b7027d4976a5600c683f261b7203408fcaff540ba981f0c5757cc692f78","abstract_canon_sha256":"70738c114e26bb218de5e5ea5cf534126221a9584b2cdb8a915d7d635fc1e0d9"},"schema_version":"1.0"},"canonical_sha256":"67954bdebbf1e6ddacfdd83b15366741914ee3dc515a3aa83024fb925533adef","source":{"kind":"arxiv","id":"1612.05620","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05620","created_at":"2026-05-18T00:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05620v2","created_at":"2026-05-18T00:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05620","created_at":"2026-05-18T00:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"M6KUXXV36HTN","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"M6KUXXV36HTN3LH5","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"M6KUXXV3","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:M6KUXXV36HTN3LH53A5RKNTHIG","target":"record","payload":{"canonical_record":{"source":{"id":"1612.05620","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-16T20:23:00Z","cross_cats_sorted":[],"title_canon_sha256":"5c528b7027d4976a5600c683f261b7203408fcaff540ba981f0c5757cc692f78","abstract_canon_sha256":"70738c114e26bb218de5e5ea5cf534126221a9584b2cdb8a915d7d635fc1e0d9"},"schema_version":"1.0"},"canonical_sha256":"67954bdebbf1e6ddacfdd83b15366741914ee3dc515a3aa83024fb925533adef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:25.481931Z","signature_b64":"aILVBAXoYS4D0HZJndI8d0d800nTNmx1Uqzon6Tv+mtRWK/mVCUC0Zt5HC71hED3wOqQYFBkue02WQ1aLirIBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67954bdebbf1e6ddacfdd83b15366741914ee3dc515a3aa83024fb925533adef","last_reissued_at":"2026-05-18T00:41:25.481282Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:25.481282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.05620","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":"2026-05-18T00:41:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ncMBvuT82+/z7B4UYpKXVw1QD+fHdzQGDtxYj8viir4jRW0t+3q5gsFOFCt8jhMkTUBOz03rYn68OeETTqWuBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:13:46.951712Z"},"content_sha256":"5df0a6d436021f974d65c7b4402cb6611c2841579d89d11022c55066195c4e72","schema_version":"1.0","event_id":"sha256:5df0a6d436021f974d65c7b4402cb6611c2841579d89d11022c55066195c4e72"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:M6KUXXV36HTN3LH53A5RKNTHIG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On D.Y. Gao and X. Lu paper \"On the extrema of a nonconvex functional with double-well potential in 1D\"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Constantin Zalinescu","submitted_at":"2016-12-16T20:23:00Z","abstract_excerpt":"The aim of this paper is to discuss the main result in the paper by D.Y. Gao and X. Lu [On the extrema of a nonconvex functional with double-well potential in 1D, Z. Angew. Math. Phys. (2016) 67:62]. More precisely we provide a detailed study of the problem considered in that paper, pointing out the importance of the norm on the space $C^{1}[a,b]$; because no norm (topology) is mentioned on $C^{1}[a,b]$ we look at it as being a subspace of $W^{1,p}(a,b)$ for $p\\in [1,\\infty]$ endowed with its usual norm. We show that the objective function has not local extrema with the mentioned constraints f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05620","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":"2026-05-18T00:41:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AeyRc8CfSZTBEsiMswoagKyZiULwo1kkYFKwgqzm+fxgXNfSx2e6b60AdNxx2CKlxgCJ9aAcYFxC8KM6MJRHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:13:46.952491Z"},"content_sha256":"76f63b8789d23773a4140a60c2cbfd718fc8709b172874909abb918a84494223","schema_version":"1.0","event_id":"sha256:76f63b8789d23773a4140a60c2cbfd718fc8709b172874909abb918a84494223"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M6KUXXV36HTN3LH53A5RKNTHIG/bundle.json","state_url":"https://pith.science/pith/M6KUXXV36HTN3LH53A5RKNTHIG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M6KUXXV36HTN3LH53A5RKNTHIG/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":"2026-06-10T10:13:46Z","links":{"resolver":"https://pith.science/pith/M6KUXXV36HTN3LH53A5RKNTHIG","bundle":"https://pith.science/pith/M6KUXXV36HTN3LH53A5RKNTHIG/bundle.json","state":"https://pith.science/pith/M6KUXXV36HTN3LH53A5RKNTHIG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M6KUXXV36HTN3LH53A5RKNTHIG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:M6KUXXV36HTN3LH53A5RKNTHIG","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":"70738c114e26bb218de5e5ea5cf534126221a9584b2cdb8a915d7d635fc1e0d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-16T20:23:00Z","title_canon_sha256":"5c528b7027d4976a5600c683f261b7203408fcaff540ba981f0c5757cc692f78"},"schema_version":"1.0","source":{"id":"1612.05620","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05620","created_at":"2026-05-18T00:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05620v2","created_at":"2026-05-18T00:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05620","created_at":"2026-05-18T00:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"M6KUXXV36HTN","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"M6KUXXV36HTN3LH5","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"M6KUXXV3","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:76f63b8789d23773a4140a60c2cbfd718fc8709b172874909abb918a84494223","target":"graph","created_at":"2026-05-18T00:41:25Z","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":"The aim of this paper is to discuss the main result in the paper by D.Y. Gao and X. Lu [On the extrema of a nonconvex functional with double-well potential in 1D, Z. Angew. Math. Phys. (2016) 67:62]. More precisely we provide a detailed study of the problem considered in that paper, pointing out the importance of the norm on the space $C^{1}[a,b]$; because no norm (topology) is mentioned on $C^{1}[a,b]$ we look at it as being a subspace of $W^{1,p}(a,b)$ for $p\\in [1,\\infty]$ endowed with its usual norm. We show that the objective function has not local extrema with the mentioned constraints f","authors_text":"Constantin Zalinescu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-16T20:23:00Z","title":"On D.Y. Gao and X. Lu paper \"On the extrema of a nonconvex functional with double-well potential in 1D\""},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05620","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":"sha256:5df0a6d436021f974d65c7b4402cb6611c2841579d89d11022c55066195c4e72","target":"record","created_at":"2026-05-18T00:41:25Z","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":"70738c114e26bb218de5e5ea5cf534126221a9584b2cdb8a915d7d635fc1e0d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-16T20:23:00Z","title_canon_sha256":"5c528b7027d4976a5600c683f261b7203408fcaff540ba981f0c5757cc692f78"},"schema_version":"1.0","source":{"id":"1612.05620","kind":"arxiv","version":2}},"canonical_sha256":"67954bdebbf1e6ddacfdd83b15366741914ee3dc515a3aa83024fb925533adef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67954bdebbf1e6ddacfdd83b15366741914ee3dc515a3aa83024fb925533adef","first_computed_at":"2026-05-18T00:41:25.481282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:25.481282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aILVBAXoYS4D0HZJndI8d0d800nTNmx1Uqzon6Tv+mtRWK/mVCUC0Zt5HC71hED3wOqQYFBkue02WQ1aLirIBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:25.481931Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.05620","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5df0a6d436021f974d65c7b4402cb6611c2841579d89d11022c55066195c4e72","sha256:76f63b8789d23773a4140a60c2cbfd718fc8709b172874909abb918a84494223"],"state_sha256":"822ea65ced57d646a248722abf86c29217d9e27a7127c0a8d898f9da4bb173f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OceprIK7tsJzhJwAysXwtoojCMBHkpXZzzaCJtuogVjqaaR3NGfE0IB1J5KsnAJviVfCJ/fd+zNjs0iHZqrLBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T10:13:46.956891Z","bundle_sha256":"21cbef1bf2f0d0263da9d222567c000cc429446eeefd3fc321e202804ac831b5"}}