{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:EBVIICP4LG6EQBDIU554L33NW5","short_pith_number":"pith:EBVIICP4","canonical_record":{"source":{"id":"1608.08363","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2016-08-30T08:33:31Z","cross_cats_sorted":["math-ph","math.MP","physics.comp-ph"],"title_canon_sha256":"c17a625ee05c5d7260cb153e31ebac3a596ff72818d53491736a4417fc6336c6","abstract_canon_sha256":"f6a1cae0c2bd18d0bfcee13a3b895d323b76b2a1f216c94beff14a641f8474ca"},"schema_version":"1.0"},"canonical_sha256":"206a8409fc59bc480468a77bc5ef6db77702958c95fb2fea2a61d94cdb770086","source":{"kind":"arxiv","id":"1608.08363","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08363","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08363v1","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08363","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"EBVIICP4LG6E","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EBVIICP4LG6EQBDI","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EBVIICP4","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:EBVIICP4LG6EQBDIU554L33NW5","target":"record","payload":{"canonical_record":{"source":{"id":"1608.08363","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2016-08-30T08:33:31Z","cross_cats_sorted":["math-ph","math.MP","physics.comp-ph"],"title_canon_sha256":"c17a625ee05c5d7260cb153e31ebac3a596ff72818d53491736a4417fc6336c6","abstract_canon_sha256":"f6a1cae0c2bd18d0bfcee13a3b895d323b76b2a1f216c94beff14a641f8474ca"},"schema_version":"1.0"},"canonical_sha256":"206a8409fc59bc480468a77bc5ef6db77702958c95fb2fea2a61d94cdb770086","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:18.282366Z","signature_b64":"oMWSzHWC4ga3zURPR5Hnu2MUmQU6pkBPOHx+f7dbHUFO2AiHtl1t9D+3DXVANLA8vmSRZaEt/YRDtdGiz9dkCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"206a8409fc59bc480468a77bc5ef6db77702958c95fb2fea2a61d94cdb770086","last_reissued_at":"2026-05-18T00:41:18.281763Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:18.281763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.08363","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":"2026-05-18T00:41:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UGChFdW8qkdpcwG/3t/rmpcq7BvM7LvPTwXq+8hbcaJ/FIbznBx2b9zzgD2AGSbipp5c9aMieFnmltpMS5N4BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T19:57:25.517889Z"},"content_sha256":"27e1a298ca6ab0a75dd600f229a4476a6a4ed3d08df9ab253dfa971400ee5d3f","schema_version":"1.0","event_id":"sha256:27e1a298ca6ab0a75dd600f229a4476a6a4ed3d08df9ab253dfa971400ee5d3f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:EBVIICP4LG6EQBDIU554L33NW5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Identifying space-dependent coefficients and the order of fractionality in fractional advection diffusion equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.comp-ph"],"primary_cat":"physics.class-ph","authors_text":"Alain Cartalade, Boris Maryshev, Christelle Latrille, Marie-Christine N\\'eel","submitted_at":"2016-08-30T08:33:31Z","abstract_excerpt":"Tracer tests in natural porous media sometimes show abnormalities that suggest considering a fractional variant of the Advection Diffusion Equation supplemented by a time derivative of non-integer order. We are describing an inverse method for this equation: it finds the order of the fractional derivative and the coefficients that achieve minimum discrepancy between solution and tracer data. Using an adjoint equation divides the computational effort by an amount proportional to the number of freedom degrees, which becomes large when some coefficients depend on space. Method accuracy is checked"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08363","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":"2026-05-18T00:41:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ldxSoA+vT4EUjbHETTt4uKWPElTSZ+DhQoGDft11kzrhWBW1v/f3/gd103WsOGXMdb0oi9/s1PXqtuuNkNRGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T19:57:25.518233Z"},"content_sha256":"85a6f2b022318c68912f7eee3ac5a9a769f68ef3574a7523322b164bc6af0218","schema_version":"1.0","event_id":"sha256:85a6f2b022318c68912f7eee3ac5a9a769f68ef3574a7523322b164bc6af0218"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EBVIICP4LG6EQBDIU554L33NW5/bundle.json","state_url":"https://pith.science/pith/EBVIICP4LG6EQBDIU554L33NW5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EBVIICP4LG6EQBDIU554L33NW5/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":"2026-06-27T19:57:25Z","links":{"resolver":"https://pith.science/pith/EBVIICP4LG6EQBDIU554L33NW5","bundle":"https://pith.science/pith/EBVIICP4LG6EQBDIU554L33NW5/bundle.json","state":"https://pith.science/pith/EBVIICP4LG6EQBDIU554L33NW5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EBVIICP4LG6EQBDIU554L33NW5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EBVIICP4LG6EQBDIU554L33NW5","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":"f6a1cae0c2bd18d0bfcee13a3b895d323b76b2a1f216c94beff14a641f8474ca","cross_cats_sorted":["math-ph","math.MP","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2016-08-30T08:33:31Z","title_canon_sha256":"c17a625ee05c5d7260cb153e31ebac3a596ff72818d53491736a4417fc6336c6"},"schema_version":"1.0","source":{"id":"1608.08363","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08363","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08363v1","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08363","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"EBVIICP4LG6E","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EBVIICP4LG6EQBDI","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EBVIICP4","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:85a6f2b022318c68912f7eee3ac5a9a769f68ef3574a7523322b164bc6af0218","target":"graph","created_at":"2026-05-18T00:41:18Z","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":"Tracer tests in natural porous media sometimes show abnormalities that suggest considering a fractional variant of the Advection Diffusion Equation supplemented by a time derivative of non-integer order. We are describing an inverse method for this equation: it finds the order of the fractional derivative and the coefficients that achieve minimum discrepancy between solution and tracer data. Using an adjoint equation divides the computational effort by an amount proportional to the number of freedom degrees, which becomes large when some coefficients depend on space. Method accuracy is checked","authors_text":"Alain Cartalade, Boris Maryshev, Christelle Latrille, Marie-Christine N\\'eel","cross_cats":["math-ph","math.MP","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2016-08-30T08:33:31Z","title":"Identifying space-dependent coefficients and the order of fractionality in fractional advection diffusion equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08363","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":"sha256:27e1a298ca6ab0a75dd600f229a4476a6a4ed3d08df9ab253dfa971400ee5d3f","target":"record","created_at":"2026-05-18T00:41:18Z","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":"f6a1cae0c2bd18d0bfcee13a3b895d323b76b2a1f216c94beff14a641f8474ca","cross_cats_sorted":["math-ph","math.MP","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2016-08-30T08:33:31Z","title_canon_sha256":"c17a625ee05c5d7260cb153e31ebac3a596ff72818d53491736a4417fc6336c6"},"schema_version":"1.0","source":{"id":"1608.08363","kind":"arxiv","version":1}},"canonical_sha256":"206a8409fc59bc480468a77bc5ef6db77702958c95fb2fea2a61d94cdb770086","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"206a8409fc59bc480468a77bc5ef6db77702958c95fb2fea2a61d94cdb770086","first_computed_at":"2026-05-18T00:41:18.281763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:18.281763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oMWSzHWC4ga3zURPR5Hnu2MUmQU6pkBPOHx+f7dbHUFO2AiHtl1t9D+3DXVANLA8vmSRZaEt/YRDtdGiz9dkCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:18.282366Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.08363","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27e1a298ca6ab0a75dd600f229a4476a6a4ed3d08df9ab253dfa971400ee5d3f","sha256:85a6f2b022318c68912f7eee3ac5a9a769f68ef3574a7523322b164bc6af0218"],"state_sha256":"030c35acd5be8051d98f8db0397c861762a719bf24b966f28104fcd94711d29c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qPtw7Y6mWRP9mpL8j/o68oXlW7lpCu+S5sFQ0qJi0FJFf+vJViD8E4hte7pk85yr1O7r/NarY5b64SZONyGJDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T19:57:25.520274Z","bundle_sha256":"c9d3dca15d0f5866397d221062dd3bac4d03b5ab094dcaec171aef6506f416cc"}}