{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:PQKJSUIBRZLFOU4AVTD2JSSF7S","short_pith_number":"pith:PQKJSUIB","canonical_record":{"source":{"id":"1412.4720","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-12-15T19:00:18Z","cross_cats_sorted":[],"title_canon_sha256":"91f07a884552436667fc207cfa815a2195c4440a8248624ffb2879c1872947bf","abstract_canon_sha256":"8d65c4cda1e82f437d7e6a6e079674a44cb142980fbc69ab49ac2dc4d3d74c25"},"schema_version":"1.0"},"canonical_sha256":"7c149951018e56575380acc7a4ca45fcb1122e2d244a62032565fd4a4d53b45a","source":{"kind":"arxiv","id":"1412.4720","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.4720","created_at":"2026-05-18T02:04:02Z"},{"alias_kind":"arxiv_version","alias_value":"1412.4720v1","created_at":"2026-05-18T02:04:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.4720","created_at":"2026-05-18T02:04:02Z"},{"alias_kind":"pith_short_12","alias_value":"PQKJSUIBRZLF","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PQKJSUIBRZLFOU4A","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PQKJSUIB","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:PQKJSUIBRZLFOU4AVTD2JSSF7S","target":"record","payload":{"canonical_record":{"source":{"id":"1412.4720","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-12-15T19:00:18Z","cross_cats_sorted":[],"title_canon_sha256":"91f07a884552436667fc207cfa815a2195c4440a8248624ffb2879c1872947bf","abstract_canon_sha256":"8d65c4cda1e82f437d7e6a6e079674a44cb142980fbc69ab49ac2dc4d3d74c25"},"schema_version":"1.0"},"canonical_sha256":"7c149951018e56575380acc7a4ca45fcb1122e2d244a62032565fd4a4d53b45a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:02.273443Z","signature_b64":"2kUzs704rEXfdEsy9ujRjqnkGOCKZelXKU+Jf+4GQk/jDXPYYH9c3LrRmAZJ4AEY+56HOuj8Xz0tlFpJFvtmAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c149951018e56575380acc7a4ca45fcb1122e2d244a62032565fd4a4d53b45a","last_reissued_at":"2026-05-18T02:04:02.272700Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:02.272700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.4720","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":"2026-05-18T02:04:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eNHRFPEW13W5w0ftr0LfPqb9IHD2UPWBZ57u3ApUDJD3Yb6HwUGykjfPMKVlC035RRYPbhGv4Up45l2QAXIfAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:45:10.263342Z"},"content_sha256":"2202a39cc65a612d642f947653871c13ac2eb43b3a1eaf6f88b5a0c891ac37e7","schema_version":"1.0","event_id":"sha256:2202a39cc65a612d642f947653871c13ac2eb43b3a1eaf6f88b5a0c891ac37e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:PQKJSUIBRZLFOU4AVTD2JSSF7S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Advection diffusion equation with absorbing boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"John Grant, Michael Wilkinson","submitted_at":"2014-12-15T19:00:18Z","abstract_excerpt":"We consider a spatially homogeneous advection-diffusion equation in which the diffusion tensor and drift velocity are time-independent, but otherwise general. We derive asymptotic expressions, valid at large distances from a steady point source, for the flux onto a completely permeable boundary and onto an absorbing boundary. The absorbing case is treated by making a source of antiparticles at the boundary. In both cases there is an exponential decay as the distance from the source increases; we find that the exponent is the same for both boundary conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4720","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":"2026-05-18T02:04:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a3l7YiBpPbk4/dhesmM6TvnPQDFtCWpjxoer55i/TldxnA6WwgkvJVOR0YNYXpPwvpVH2Qg20i7cRi7ow0zADA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:45:10.263939Z"},"content_sha256":"fc316b9a62dd8f535b79a46fa8b6f01c715860205696354798e4222bf7e78273","schema_version":"1.0","event_id":"sha256:fc316b9a62dd8f535b79a46fa8b6f01c715860205696354798e4222bf7e78273"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PQKJSUIBRZLFOU4AVTD2JSSF7S/bundle.json","state_url":"https://pith.science/pith/PQKJSUIBRZLFOU4AVTD2JSSF7S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PQKJSUIBRZLFOU4AVTD2JSSF7S/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":"2026-06-06T14:45:10Z","links":{"resolver":"https://pith.science/pith/PQKJSUIBRZLFOU4AVTD2JSSF7S","bundle":"https://pith.science/pith/PQKJSUIBRZLFOU4AVTD2JSSF7S/bundle.json","state":"https://pith.science/pith/PQKJSUIBRZLFOU4AVTD2JSSF7S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PQKJSUIBRZLFOU4AVTD2JSSF7S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PQKJSUIBRZLFOU4AVTD2JSSF7S","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":"8d65c4cda1e82f437d7e6a6e079674a44cb142980fbc69ab49ac2dc4d3d74c25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-12-15T19:00:18Z","title_canon_sha256":"91f07a884552436667fc207cfa815a2195c4440a8248624ffb2879c1872947bf"},"schema_version":"1.0","source":{"id":"1412.4720","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.4720","created_at":"2026-05-18T02:04:02Z"},{"alias_kind":"arxiv_version","alias_value":"1412.4720v1","created_at":"2026-05-18T02:04:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.4720","created_at":"2026-05-18T02:04:02Z"},{"alias_kind":"pith_short_12","alias_value":"PQKJSUIBRZLF","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PQKJSUIBRZLFOU4A","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PQKJSUIB","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:fc316b9a62dd8f535b79a46fa8b6f01c715860205696354798e4222bf7e78273","target":"graph","created_at":"2026-05-18T02:04:02Z","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 consider a spatially homogeneous advection-diffusion equation in which the diffusion tensor and drift velocity are time-independent, but otherwise general. We derive asymptotic expressions, valid at large distances from a steady point source, for the flux onto a completely permeable boundary and onto an absorbing boundary. The absorbing case is treated by making a source of antiparticles at the boundary. In both cases there is an exponential decay as the distance from the source increases; we find that the exponent is the same for both boundary conditions.","authors_text":"John Grant, Michael Wilkinson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-12-15T19:00:18Z","title":"Advection diffusion equation with absorbing boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4720","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":"sha256:2202a39cc65a612d642f947653871c13ac2eb43b3a1eaf6f88b5a0c891ac37e7","target":"record","created_at":"2026-05-18T02:04:02Z","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":"8d65c4cda1e82f437d7e6a6e079674a44cb142980fbc69ab49ac2dc4d3d74c25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-12-15T19:00:18Z","title_canon_sha256":"91f07a884552436667fc207cfa815a2195c4440a8248624ffb2879c1872947bf"},"schema_version":"1.0","source":{"id":"1412.4720","kind":"arxiv","version":1}},"canonical_sha256":"7c149951018e56575380acc7a4ca45fcb1122e2d244a62032565fd4a4d53b45a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c149951018e56575380acc7a4ca45fcb1122e2d244a62032565fd4a4d53b45a","first_computed_at":"2026-05-18T02:04:02.272700Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:02.272700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2kUzs704rEXfdEsy9ujRjqnkGOCKZelXKU+Jf+4GQk/jDXPYYH9c3LrRmAZJ4AEY+56HOuj8Xz0tlFpJFvtmAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:02.273443Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.4720","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2202a39cc65a612d642f947653871c13ac2eb43b3a1eaf6f88b5a0c891ac37e7","sha256:fc316b9a62dd8f535b79a46fa8b6f01c715860205696354798e4222bf7e78273"],"state_sha256":"555eca5eb6cf232f8fba0fd435ddf4a4134bfa8c00d0ec2ad5686abd35c83c82"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Uw5TVzjPR3Fwil4I+CM0KzWXWffB00jD/ohagSHPDCzntplaahsUNfDydxjznUxQoa9TxmAxEJd7FGuj5T3Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T14:45:10.266778Z","bundle_sha256":"60a47fb25327c3b2f842b99b25faf03eb9bbb5c8806deb5e3ea95f2b2e4416b3"}}