{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:VFPKPZON5PAC3GUMXMXKZLFPAB","short_pith_number":"pith:VFPKPZON","canonical_record":{"source":{"id":"1512.06540","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-21T09:32:51Z","cross_cats_sorted":["math.DS","math.FA"],"title_canon_sha256":"db317aaab63d7034ae9075bb77aa8420bdbb772333870fb9dcd8c601fc623f59","abstract_canon_sha256":"431a4ff95481f6abe9a2fa0c661f820d51f6a3cdda550d9705b508e73679ff55"},"schema_version":"1.0"},"canonical_sha256":"a95ea7e5cdebc02d9a8cbb2eacacaf007ff8d93cd69026654649b1288d423474","source":{"kind":"arxiv","id":"1512.06540","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.06540","created_at":"2026-05-18T01:24:00Z"},{"alias_kind":"arxiv_version","alias_value":"1512.06540v1","created_at":"2026-05-18T01:24:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06540","created_at":"2026-05-18T01:24:00Z"},{"alias_kind":"pith_short_12","alias_value":"VFPKPZON5PAC","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"VFPKPZON5PAC3GUM","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"VFPKPZON","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:VFPKPZON5PAC3GUMXMXKZLFPAB","target":"record","payload":{"canonical_record":{"source":{"id":"1512.06540","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-21T09:32:51Z","cross_cats_sorted":["math.DS","math.FA"],"title_canon_sha256":"db317aaab63d7034ae9075bb77aa8420bdbb772333870fb9dcd8c601fc623f59","abstract_canon_sha256":"431a4ff95481f6abe9a2fa0c661f820d51f6a3cdda550d9705b508e73679ff55"},"schema_version":"1.0"},"canonical_sha256":"a95ea7e5cdebc02d9a8cbb2eacacaf007ff8d93cd69026654649b1288d423474","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:00.262141Z","signature_b64":"p29SXYMEssbs0ME4YcRyK8YMxbOU3qhZroJ4jAW/+DS4iTfgYhRfM5LOXqRhOs+8LU7UQcf93Q3x1c+/5VHyBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a95ea7e5cdebc02d9a8cbb2eacacaf007ff8d93cd69026654649b1288d423474","last_reissued_at":"2026-05-18T01:24:00.261447Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:00.261447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.06540","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":"2026-05-18T01:24:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w/3bZScceK8a/OJ25tGOe4KLAiB8ZH5G8cK/ghDEW8NTs5zgv6Bdw7w9VOJgNtj8CnzkVAEQdzEESDdc+lm+CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:19:37.367615Z"},"content_sha256":"994fc7a74b989001f1c5012eb5476eee0550d05c84c2975b043c0c5c3a35ce7e","schema_version":"1.0","event_id":"sha256:994fc7a74b989001f1c5012eb5476eee0550d05c84c2975b043c0c5c3a35ce7e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:VFPKPZON5PAC3GUMXMXKZLFPAB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some simple problems for the next generations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA"],"primary_cat":"math.AP","authors_text":"Alain Haraux (LJLL)","submitted_at":"2015-12-21T09:32:51Z","abstract_excerpt":"A list of open problems on global behavior in time of some evolution systems, mainly governed by P.D.E, is given together with some background information explaining the context in which these problems appeared. The common characteristic of these problems is that they appeared a long time ago in the personnal research of the author and received almost no answer till then at the exception of very partial results which are listed to help the readers' understanding of the difficulties involved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06540","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":"2026-05-18T01:24:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dhmd+kj7rMaab7A8On6T7cJQ+/+Q0PVOj++JmBpGoScbV3wlXQcWID+j35gMlNaRQpbPHPidvhdIrPRm+Qh4BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:19:37.367960Z"},"content_sha256":"e52d6c380c9a7568e206833d724bf98c282259d256c904bd3f2cf82826893467","schema_version":"1.0","event_id":"sha256:e52d6c380c9a7568e206833d724bf98c282259d256c904bd3f2cf82826893467"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VFPKPZON5PAC3GUMXMXKZLFPAB/bundle.json","state_url":"https://pith.science/pith/VFPKPZON5PAC3GUMXMXKZLFPAB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VFPKPZON5PAC3GUMXMXKZLFPAB/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":"2026-07-01T21:19:37Z","links":{"resolver":"https://pith.science/pith/VFPKPZON5PAC3GUMXMXKZLFPAB","bundle":"https://pith.science/pith/VFPKPZON5PAC3GUMXMXKZLFPAB/bundle.json","state":"https://pith.science/pith/VFPKPZON5PAC3GUMXMXKZLFPAB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VFPKPZON5PAC3GUMXMXKZLFPAB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VFPKPZON5PAC3GUMXMXKZLFPAB","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":"431a4ff95481f6abe9a2fa0c661f820d51f6a3cdda550d9705b508e73679ff55","cross_cats_sorted":["math.DS","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-21T09:32:51Z","title_canon_sha256":"db317aaab63d7034ae9075bb77aa8420bdbb772333870fb9dcd8c601fc623f59"},"schema_version":"1.0","source":{"id":"1512.06540","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.06540","created_at":"2026-05-18T01:24:00Z"},{"alias_kind":"arxiv_version","alias_value":"1512.06540v1","created_at":"2026-05-18T01:24:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06540","created_at":"2026-05-18T01:24:00Z"},{"alias_kind":"pith_short_12","alias_value":"VFPKPZON5PAC","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"VFPKPZON5PAC3GUM","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"VFPKPZON","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:e52d6c380c9a7568e206833d724bf98c282259d256c904bd3f2cf82826893467","target":"graph","created_at":"2026-05-18T01:24:00Z","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":"A list of open problems on global behavior in time of some evolution systems, mainly governed by P.D.E, is given together with some background information explaining the context in which these problems appeared. The common characteristic of these problems is that they appeared a long time ago in the personnal research of the author and received almost no answer till then at the exception of very partial results which are listed to help the readers' understanding of the difficulties involved.","authors_text":"Alain Haraux (LJLL)","cross_cats":["math.DS","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-21T09:32:51Z","title":"Some simple problems for the next generations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06540","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":"sha256:994fc7a74b989001f1c5012eb5476eee0550d05c84c2975b043c0c5c3a35ce7e","target":"record","created_at":"2026-05-18T01:24:00Z","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":"431a4ff95481f6abe9a2fa0c661f820d51f6a3cdda550d9705b508e73679ff55","cross_cats_sorted":["math.DS","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-21T09:32:51Z","title_canon_sha256":"db317aaab63d7034ae9075bb77aa8420bdbb772333870fb9dcd8c601fc623f59"},"schema_version":"1.0","source":{"id":"1512.06540","kind":"arxiv","version":1}},"canonical_sha256":"a95ea7e5cdebc02d9a8cbb2eacacaf007ff8d93cd69026654649b1288d423474","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a95ea7e5cdebc02d9a8cbb2eacacaf007ff8d93cd69026654649b1288d423474","first_computed_at":"2026-05-18T01:24:00.261447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:00.261447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p29SXYMEssbs0ME4YcRyK8YMxbOU3qhZroJ4jAW/+DS4iTfgYhRfM5LOXqRhOs+8LU7UQcf93Q3x1c+/5VHyBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:00.262141Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.06540","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:994fc7a74b989001f1c5012eb5476eee0550d05c84c2975b043c0c5c3a35ce7e","sha256:e52d6c380c9a7568e206833d724bf98c282259d256c904bd3f2cf82826893467"],"state_sha256":"105ced7eaa0703473c5435f0e6a3049899feb56ea11dc0244996170192b1d623"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yGHuUBbQrm9MgnPrNvVjKnxYpo/D9UzDdGMx+e9eXB9DsU//faHfZOPXYp3QL8C4hP+44weL/jkKllYMyUVSDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T21:19:37.370142Z","bundle_sha256":"a607b858b00f0a68dc45a65287771f08d86d76913d3a8c177119d243281232b6"}}