{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:L57OI3ZL3BS35KMLLS5EHKW4HC","short_pith_number":"pith:L57OI3ZL","canonical_record":{"source":{"id":"1604.04903","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"q-bio.QM","submitted_at":"2016-04-17T18:05:02Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"971d40b95fcc8013f68187bdc3690e8bdc6c8dfddbcc23ef991eab8c41ce4afe","abstract_canon_sha256":"4acfa96d23c06c409d426126ddb2c97e6098ab5f3481d64064c87d6593cc111e"},"schema_version":"1.0"},"canonical_sha256":"5f7ee46f2bd865bea98b5cba43aadc38812a9ff4a5638681d339373dc9ae0c96","source":{"kind":"arxiv","id":"1604.04903","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.04903","created_at":"2026-05-18T00:35:35Z"},{"alias_kind":"arxiv_version","alias_value":"1604.04903v1","created_at":"2026-05-18T00:35:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.04903","created_at":"2026-05-18T00:35:35Z"},{"alias_kind":"pith_short_12","alias_value":"L57OI3ZL3BS3","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"L57OI3ZL3BS35KML","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"L57OI3ZL","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:L57OI3ZL3BS35KMLLS5EHKW4HC","target":"record","payload":{"canonical_record":{"source":{"id":"1604.04903","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"q-bio.QM","submitted_at":"2016-04-17T18:05:02Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"971d40b95fcc8013f68187bdc3690e8bdc6c8dfddbcc23ef991eab8c41ce4afe","abstract_canon_sha256":"4acfa96d23c06c409d426126ddb2c97e6098ab5f3481d64064c87d6593cc111e"},"schema_version":"1.0"},"canonical_sha256":"5f7ee46f2bd865bea98b5cba43aadc38812a9ff4a5638681d339373dc9ae0c96","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:35.809417Z","signature_b64":"nwa+u1uJmKIC8VEiKxcF+bcQ2SEDg/Px+gd9y5dqF3ybm87a0+ERtzwVkiMXyjUee97LScV4QSgZz6Gg0C8ZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f7ee46f2bd865bea98b5cba43aadc38812a9ff4a5638681d339373dc9ae0c96","last_reissued_at":"2026-05-18T00:35:35.808987Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:35.808987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.04903","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":"2026-05-18T00:35:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kHs8Fhfu0hUIkX6FqOTW8wEYXXNGrqpugqhNpdTrNT9wTex5VHiEMnVJ9ipXzNOFuO8BEcEgVtKNIZxpLyibAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T14:12:28.219809Z"},"content_sha256":"06dd664e8abcde91a82ff9fe37a5bf7757a5900333cd1b0da78ff914cd28e6f2","schema_version":"1.0","event_id":"sha256:06dd664e8abcde91a82ff9fe37a5bf7757a5900333cd1b0da78ff914cd28e6f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:L57OI3ZL3BS35KMLLS5EHKW4HC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Path integral approach to theories of diffusion-influenced reactions","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"q-bio.QM","authors_text":"Martin Meier-Schellersheim, Thorsten Pr\\\"ustel","submitted_at":"2016-04-17T18:05:02Z","abstract_excerpt":"The path decomposition expansion represents the propagator of the irreversible reaction as a convolution of the first-passage, last-passage and rebinding time probability densities. Using path integral technique, we give an elementary, yet rigorous, proof of the path decomposition expansion of the Green's functions describing the non-reactive case and the irreversible reaction of an isolated pair of molecules. To this end, we exploit the connection between boundary value problems and interaction potential problems with $\\delta$- and $\\delta'$-function perturbation. In particular, we employ a k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04903","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":"2026-05-18T00:35:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5l3oUH9T0UMrHZS7C/+7Rucrti/oDPynMvytWcC8VVMHptf+ZLLdjNsOUq+3U5NDs4Gb8tG8lT3vzUFS68LcDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T14:12:28.220149Z"},"content_sha256":"84ff2920040b9d23b6c560a9b97dca81233075ec4b62fefe90bb58580dffa7c5","schema_version":"1.0","event_id":"sha256:84ff2920040b9d23b6c560a9b97dca81233075ec4b62fefe90bb58580dffa7c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L57OI3ZL3BS35KMLLS5EHKW4HC/bundle.json","state_url":"https://pith.science/pith/L57OI3ZL3BS35KMLLS5EHKW4HC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L57OI3ZL3BS35KMLLS5EHKW4HC/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":"2026-06-29T14:12:28Z","links":{"resolver":"https://pith.science/pith/L57OI3ZL3BS35KMLLS5EHKW4HC","bundle":"https://pith.science/pith/L57OI3ZL3BS35KMLLS5EHKW4HC/bundle.json","state":"https://pith.science/pith/L57OI3ZL3BS35KMLLS5EHKW4HC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L57OI3ZL3BS35KMLLS5EHKW4HC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:L57OI3ZL3BS35KMLLS5EHKW4HC","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":"4acfa96d23c06c409d426126ddb2c97e6098ab5f3481d64064c87d6593cc111e","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"q-bio.QM","submitted_at":"2016-04-17T18:05:02Z","title_canon_sha256":"971d40b95fcc8013f68187bdc3690e8bdc6c8dfddbcc23ef991eab8c41ce4afe"},"schema_version":"1.0","source":{"id":"1604.04903","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.04903","created_at":"2026-05-18T00:35:35Z"},{"alias_kind":"arxiv_version","alias_value":"1604.04903v1","created_at":"2026-05-18T00:35:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.04903","created_at":"2026-05-18T00:35:35Z"},{"alias_kind":"pith_short_12","alias_value":"L57OI3ZL3BS3","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"L57OI3ZL3BS35KML","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"L57OI3ZL","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:84ff2920040b9d23b6c560a9b97dca81233075ec4b62fefe90bb58580dffa7c5","target":"graph","created_at":"2026-05-18T00:35:35Z","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 path decomposition expansion represents the propagator of the irreversible reaction as a convolution of the first-passage, last-passage and rebinding time probability densities. Using path integral technique, we give an elementary, yet rigorous, proof of the path decomposition expansion of the Green's functions describing the non-reactive case and the irreversible reaction of an isolated pair of molecules. To this end, we exploit the connection between boundary value problems and interaction potential problems with $\\delta$- and $\\delta'$-function perturbation. In particular, we employ a k","authors_text":"Martin Meier-Schellersheim, Thorsten Pr\\\"ustel","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"q-bio.QM","submitted_at":"2016-04-17T18:05:02Z","title":"Path integral approach to theories of diffusion-influenced reactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04903","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":"sha256:06dd664e8abcde91a82ff9fe37a5bf7757a5900333cd1b0da78ff914cd28e6f2","target":"record","created_at":"2026-05-18T00:35:35Z","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":"4acfa96d23c06c409d426126ddb2c97e6098ab5f3481d64064c87d6593cc111e","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"q-bio.QM","submitted_at":"2016-04-17T18:05:02Z","title_canon_sha256":"971d40b95fcc8013f68187bdc3690e8bdc6c8dfddbcc23ef991eab8c41ce4afe"},"schema_version":"1.0","source":{"id":"1604.04903","kind":"arxiv","version":1}},"canonical_sha256":"5f7ee46f2bd865bea98b5cba43aadc38812a9ff4a5638681d339373dc9ae0c96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f7ee46f2bd865bea98b5cba43aadc38812a9ff4a5638681d339373dc9ae0c96","first_computed_at":"2026-05-18T00:35:35.808987Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:35.808987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nwa+u1uJmKIC8VEiKxcF+bcQ2SEDg/Px+gd9y5dqF3ybm87a0+ERtzwVkiMXyjUee97LScV4QSgZz6Gg0C8ZCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:35.809417Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.04903","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06dd664e8abcde91a82ff9fe37a5bf7757a5900333cd1b0da78ff914cd28e6f2","sha256:84ff2920040b9d23b6c560a9b97dca81233075ec4b62fefe90bb58580dffa7c5"],"state_sha256":"4ff9b5a41bfe947ba39a6f688b78db8eb4e1283fc97ccd080b789b1705b14cb8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TJiXkCsebFum9duQEr5m7UnREt2idv4yNBlTzCDTTzKou0hWTP+t6LRXFWu5F9lJDLHl2Trs6/8KDrRZhs1yCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T14:12:28.222096Z","bundle_sha256":"c6ec8fcb02b2a70dfb02029b0aee4a9da79c72a22f58572f96aa467967f4c5bc"}}