{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:XOXFYLF26IJLU5F5POZ6MFXXWS","short_pith_number":"pith:XOXFYLF2","canonical_record":{"source":{"id":"0908.2287","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-08-17T05:56:31Z","cross_cats_sorted":["cond-mat.mtrl-sci"],"title_canon_sha256":"6d20b83ec8c6df38b7e495d031a4f6900082173f52389161f662bd0f41949d14","abstract_canon_sha256":"1325d83d01ebacaa37a47fdeceb608c2342e21b4b9cd45171942a559b319b7ab"},"schema_version":"1.0"},"canonical_sha256":"bbae5c2cbaf212ba74bd7bb3e616f7b481addc900ff5817725d9c2ebcbea044a","source":{"kind":"arxiv","id":"0908.2287","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.2287","created_at":"2026-05-18T02:12:33Z"},{"alias_kind":"arxiv_version","alias_value":"0908.2287v2","created_at":"2026-05-18T02:12:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.2287","created_at":"2026-05-18T02:12:33Z"},{"alias_kind":"pith_short_12","alias_value":"XOXFYLF26IJL","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"XOXFYLF26IJLU5F5","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"XOXFYLF2","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:XOXFYLF26IJLU5F5POZ6MFXXWS","target":"record","payload":{"canonical_record":{"source":{"id":"0908.2287","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-08-17T05:56:31Z","cross_cats_sorted":["cond-mat.mtrl-sci"],"title_canon_sha256":"6d20b83ec8c6df38b7e495d031a4f6900082173f52389161f662bd0f41949d14","abstract_canon_sha256":"1325d83d01ebacaa37a47fdeceb608c2342e21b4b9cd45171942a559b319b7ab"},"schema_version":"1.0"},"canonical_sha256":"bbae5c2cbaf212ba74bd7bb3e616f7b481addc900ff5817725d9c2ebcbea044a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:12:33.606965Z","signature_b64":"dD8LAlGTVKWjc7M4BWthScKH3v4mkPVFTA56SQAyIQajNTWdcbT51PFzktBh3ZS96Cb8oeR3Xk5HjYkrlLaJCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbae5c2cbaf212ba74bd7bb3e616f7b481addc900ff5817725d9c2ebcbea044a","last_reissued_at":"2026-05-18T02:12:33.606256Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:12:33.606256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0908.2287","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:12:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bf9299UqdsiHrVknuId5AGnDCbfO2jMhuuhKTiToiiZpS1X94ZGAMNdT8gNG+yvSApRInj1gZxY8tu23Y2mDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T12:42:05.331688Z"},"content_sha256":"4ff533827b88e0725832fb00086c5887e7f9e62599d6d2d97753347ba11c1e6c","schema_version":"1.0","event_id":"sha256:4ff533827b88e0725832fb00086c5887e7f9e62599d6d2d97753347ba11c1e6c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:XOXFYLF26IJLU5F5POZ6MFXXWS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reaction under vacancy-assisted diffusion at high quencher concentration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci"],"primary_cat":"cond-mat.stat-mech","authors_text":"Kazuhiko Seki, M. Tachiya","submitted_at":"2009-08-17T05:56:31Z","abstract_excerpt":"Theory of diffusion-mediated reactions is already established for the target problem in the dilute limit, where the immobile target is surrounded by many quenchers. For lattice random walks in the crowded situation, each quencher is surrounded by other quenchers differently. As a result, each quencher migrates differently in the presence of site blocking effects. However, in the conventional theory, such difference is ignored and quenchers are assumed to move independently of each other. In this paper, theory of diffusion-mediated reactions of target problem is developed by taking into account"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.2287","kind":"arxiv","version":2},"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":"2026-05-18T02:12:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fKGGzot7Xt1m3fGXEQflR/X8uxpueLZZ8J55rhsnWDLcXc9pVP6Xglr3WBsPrcDXiLSaVdU5ONrsqoTL7vbvAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T12:42:05.332028Z"},"content_sha256":"8ea310ce9798efa39f18fc9739fc6eff482ed2f94f63917ede6ddf6200aaf455","schema_version":"1.0","event_id":"sha256:8ea310ce9798efa39f18fc9739fc6eff482ed2f94f63917ede6ddf6200aaf455"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XOXFYLF26IJLU5F5POZ6MFXXWS/bundle.json","state_url":"https://pith.science/pith/XOXFYLF26IJLU5F5POZ6MFXXWS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XOXFYLF26IJLU5F5POZ6MFXXWS/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":"2026-06-29T12:42:05Z","links":{"resolver":"https://pith.science/pith/XOXFYLF26IJLU5F5POZ6MFXXWS","bundle":"https://pith.science/pith/XOXFYLF26IJLU5F5POZ6MFXXWS/bundle.json","state":"https://pith.science/pith/XOXFYLF26IJLU5F5POZ6MFXXWS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XOXFYLF26IJLU5F5POZ6MFXXWS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:XOXFYLF26IJLU5F5POZ6MFXXWS","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":"1325d83d01ebacaa37a47fdeceb608c2342e21b4b9cd45171942a559b319b7ab","cross_cats_sorted":["cond-mat.mtrl-sci"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-08-17T05:56:31Z","title_canon_sha256":"6d20b83ec8c6df38b7e495d031a4f6900082173f52389161f662bd0f41949d14"},"schema_version":"1.0","source":{"id":"0908.2287","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.2287","created_at":"2026-05-18T02:12:33Z"},{"alias_kind":"arxiv_version","alias_value":"0908.2287v2","created_at":"2026-05-18T02:12:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.2287","created_at":"2026-05-18T02:12:33Z"},{"alias_kind":"pith_short_12","alias_value":"XOXFYLF26IJL","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"XOXFYLF26IJLU5F5","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"XOXFYLF2","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:8ea310ce9798efa39f18fc9739fc6eff482ed2f94f63917ede6ddf6200aaf455","target":"graph","created_at":"2026-05-18T02:12:33Z","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":"Theory of diffusion-mediated reactions is already established for the target problem in the dilute limit, where the immobile target is surrounded by many quenchers. For lattice random walks in the crowded situation, each quencher is surrounded by other quenchers differently. As a result, each quencher migrates differently in the presence of site blocking effects. However, in the conventional theory, such difference is ignored and quenchers are assumed to move independently of each other. In this paper, theory of diffusion-mediated reactions of target problem is developed by taking into account","authors_text":"Kazuhiko Seki, M. Tachiya","cross_cats":["cond-mat.mtrl-sci"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-08-17T05:56:31Z","title":"Reaction under vacancy-assisted diffusion at high quencher concentration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.2287","kind":"arxiv","version":2},"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":"sha256:4ff533827b88e0725832fb00086c5887e7f9e62599d6d2d97753347ba11c1e6c","target":"record","created_at":"2026-05-18T02:12:33Z","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":"1325d83d01ebacaa37a47fdeceb608c2342e21b4b9cd45171942a559b319b7ab","cross_cats_sorted":["cond-mat.mtrl-sci"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-08-17T05:56:31Z","title_canon_sha256":"6d20b83ec8c6df38b7e495d031a4f6900082173f52389161f662bd0f41949d14"},"schema_version":"1.0","source":{"id":"0908.2287","kind":"arxiv","version":2}},"canonical_sha256":"bbae5c2cbaf212ba74bd7bb3e616f7b481addc900ff5817725d9c2ebcbea044a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bbae5c2cbaf212ba74bd7bb3e616f7b481addc900ff5817725d9c2ebcbea044a","first_computed_at":"2026-05-18T02:12:33.606256Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:12:33.606256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dD8LAlGTVKWjc7M4BWthScKH3v4mkPVFTA56SQAyIQajNTWdcbT51PFzktBh3ZS96Cb8oeR3Xk5HjYkrlLaJCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:12:33.606965Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.2287","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ff533827b88e0725832fb00086c5887e7f9e62599d6d2d97753347ba11c1e6c","sha256:8ea310ce9798efa39f18fc9739fc6eff482ed2f94f63917ede6ddf6200aaf455"],"state_sha256":"75d79d25221b49dccfd5320a7e59b98845f7f018bf102a3650bbc1fff9741f89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kHqORyXqC9m8jrDEcsz22qVMfXX9a5kHNUhsWcAA5VAydZB2kMfUBmbsDts+dbYJ8YvLr8j8bRuuCh38iIB9BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T12:42:05.333905Z","bundle_sha256":"9c46d497d6d3343de3331ebe45d4347f95b817f8fa36e2c0457f907dfa26dc97"}}