{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:FEB3PUALHLYXMABJQ56OOXYCHA","short_pith_number":"pith:FEB3PUAL","canonical_record":{"source":{"id":"2606.20875","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-18T19:06:16Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"8f386267bbb974eae968713b663dd94c23d4e7219e752d902004cbc5923073b9","abstract_canon_sha256":"41b2887786f22101067c9417fbc3860bb279016b4fd571e8110996f90730dc03"},"schema_version":"1.0"},"canonical_sha256":"2903b7d00b3af1760029877ce75f023829ce82ac3e3686bb4bda6e8a37e70e4f","source":{"kind":"arxiv","id":"2606.20875","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.20875","created_at":"2026-06-23T00:12:01Z"},{"alias_kind":"arxiv_version","alias_value":"2606.20875v1","created_at":"2026-06-23T00:12:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.20875","created_at":"2026-06-23T00:12:01Z"},{"alias_kind":"pith_short_12","alias_value":"FEB3PUALHLYX","created_at":"2026-06-23T00:12:01Z"},{"alias_kind":"pith_short_16","alias_value":"FEB3PUALHLYXMABJ","created_at":"2026-06-23T00:12:01Z"},{"alias_kind":"pith_short_8","alias_value":"FEB3PUAL","created_at":"2026-06-23T00:12:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:FEB3PUALHLYXMABJQ56OOXYCHA","target":"record","payload":{"canonical_record":{"source":{"id":"2606.20875","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-18T19:06:16Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"8f386267bbb974eae968713b663dd94c23d4e7219e752d902004cbc5923073b9","abstract_canon_sha256":"41b2887786f22101067c9417fbc3860bb279016b4fd571e8110996f90730dc03"},"schema_version":"1.0"},"canonical_sha256":"2903b7d00b3af1760029877ce75f023829ce82ac3e3686bb4bda6e8a37e70e4f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T00:12:01.486340Z","signature_b64":"WLK625k6WtW/yngAapn/HZ7/n2B31a4t6NRM1keDVdgDJ7HZuytwoEFP5EqNunBHA8BUuznsMSphRzasbb20AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2903b7d00b3af1760029877ce75f023829ce82ac3e3686bb4bda6e8a37e70e4f","last_reissued_at":"2026-06-23T00:12:01.485992Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T00:12:01.485992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.20875","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":"2026-06-23T00:12:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t81lKiR2Bk3XHdT+7onkku2WkvvZtdoITneNznt/VMzEVNvS9u+AddL+ajUJGjHxGxj3sq1aNFz7ozNqdG9aDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T14:47:28.509066Z"},"content_sha256":"3c5e0ab147627c43f85f9b5e10944bc3741269d5b3493a4841ecda1e6fec1cea","schema_version":"1.0","event_id":"sha256:3c5e0ab147627c43f85f9b5e10944bc3741269d5b3493a4841ecda1e6fec1cea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:FEB3PUALHLYXMABJQ56OOXYCHA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inverse initial data reconstruction for a memory convection-diffusion equation via Legendre spatial reduction and Tikhonov regularization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Cong B. Van, Loc H. Nguyen, Minh-Binh Tran, Thien P.B. Nguyen","submitted_at":"2026-06-18T19:06:16Z","abstract_excerpt":"We study an inverse initial data problem for a convection-diffusion equation with memory, where the goal is to recover the unknown initial condition from final-time data. The model includes convection, an instantaneous Laplacian term, and a nonlocal-in-time memory term involving the Laplacian of the past states, which leads to a severely ill-posed backward problem. We prove uniqueness in a spatially independent coefficient setting by applying the Fourier transform and using an analyticity argument for a scalar Volterra equation. For the variable-coefficient case, we develop a computational met"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20875","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.20875/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-23T00:12:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6deWFthInBZqTBYK2FSDNggzVxRCbD2ylpuAYIDQrixPAXcVOZbsABkZ3HH83KHXpaFg6zO4VtzK5P60cJJjCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T14:47:28.509859Z"},"content_sha256":"6e24e767a55c8bff0f0d155d3e4738982e4cf7384cf45729926df94d09cdc2be","schema_version":"1.0","event_id":"sha256:6e24e767a55c8bff0f0d155d3e4738982e4cf7384cf45729926df94d09cdc2be"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FEB3PUALHLYXMABJQ56OOXYCHA/bundle.json","state_url":"https://pith.science/pith/FEB3PUALHLYXMABJQ56OOXYCHA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FEB3PUALHLYXMABJQ56OOXYCHA/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":"2026-08-14T14:47:28Z","links":{"resolver":"https://pith.science/pith/FEB3PUALHLYXMABJQ56OOXYCHA","bundle":"https://pith.science/pith/FEB3PUALHLYXMABJQ56OOXYCHA/bundle.json","state":"https://pith.science/pith/FEB3PUALHLYXMABJQ56OOXYCHA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FEB3PUALHLYXMABJQ56OOXYCHA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FEB3PUALHLYXMABJQ56OOXYCHA","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":"41b2887786f22101067c9417fbc3860bb279016b4fd571e8110996f90730dc03","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-18T19:06:16Z","title_canon_sha256":"8f386267bbb974eae968713b663dd94c23d4e7219e752d902004cbc5923073b9"},"schema_version":"1.0","source":{"id":"2606.20875","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.20875","created_at":"2026-06-23T00:12:01Z"},{"alias_kind":"arxiv_version","alias_value":"2606.20875v1","created_at":"2026-06-23T00:12:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.20875","created_at":"2026-06-23T00:12:01Z"},{"alias_kind":"pith_short_12","alias_value":"FEB3PUALHLYX","created_at":"2026-06-23T00:12:01Z"},{"alias_kind":"pith_short_16","alias_value":"FEB3PUALHLYXMABJ","created_at":"2026-06-23T00:12:01Z"},{"alias_kind":"pith_short_8","alias_value":"FEB3PUAL","created_at":"2026-06-23T00:12:01Z"}],"graph_snapshots":[{"event_id":"sha256:6e24e767a55c8bff0f0d155d3e4738982e4cf7384cf45729926df94d09cdc2be","target":"graph","created_at":"2026-06-23T00:12:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.20875/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study an inverse initial data problem for a convection-diffusion equation with memory, where the goal is to recover the unknown initial condition from final-time data. The model includes convection, an instantaneous Laplacian term, and a nonlocal-in-time memory term involving the Laplacian of the past states, which leads to a severely ill-posed backward problem. We prove uniqueness in a spatially independent coefficient setting by applying the Fourier transform and using an analyticity argument for a scalar Volterra equation. For the variable-coefficient case, we develop a computational met","authors_text":"Cong B. Van, Loc H. Nguyen, Minh-Binh Tran, Thien P.B. Nguyen","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-18T19:06:16Z","title":"Inverse initial data reconstruction for a memory convection-diffusion equation via Legendre spatial reduction and Tikhonov regularization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20875","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":"sha256:3c5e0ab147627c43f85f9b5e10944bc3741269d5b3493a4841ecda1e6fec1cea","target":"record","created_at":"2026-06-23T00:12:01Z","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":"41b2887786f22101067c9417fbc3860bb279016b4fd571e8110996f90730dc03","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-18T19:06:16Z","title_canon_sha256":"8f386267bbb974eae968713b663dd94c23d4e7219e752d902004cbc5923073b9"},"schema_version":"1.0","source":{"id":"2606.20875","kind":"arxiv","version":1}},"canonical_sha256":"2903b7d00b3af1760029877ce75f023829ce82ac3e3686bb4bda6e8a37e70e4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2903b7d00b3af1760029877ce75f023829ce82ac3e3686bb4bda6e8a37e70e4f","first_computed_at":"2026-06-23T00:12:01.485992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T00:12:01.485992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WLK625k6WtW/yngAapn/HZ7/n2B31a4t6NRM1keDVdgDJ7HZuytwoEFP5EqNunBHA8BUuznsMSphRzasbb20AQ==","signature_status":"signed_v1","signed_at":"2026-06-23T00:12:01.486340Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.20875","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c5e0ab147627c43f85f9b5e10944bc3741269d5b3493a4841ecda1e6fec1cea","sha256:6e24e767a55c8bff0f0d155d3e4738982e4cf7384cf45729926df94d09cdc2be"],"state_sha256":"3ffd3bfecbc5e1e8cb6fcc4b09876e7eea860717a3f454868ebec5e8f56a8192"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"It2v0FlnMdZitJ7AQuwIIQvoWaBr/5A1uz2o1gqhEgpO9b7yUAnbVonYDymUQdfJci0d09uDvTBllTs5v1kMAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T14:47:28.520105Z","bundle_sha256":"edb014b15caaf077f20d2dc3bb629c62d5f60e031f785ae4f25bfd21ae81e81d"}}