{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UJT7GSCQQLBZQIG74MRRDBIYJS","short_pith_number":"pith:UJT7GSCQ","canonical_record":{"source":{"id":"1509.01762","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-06T02:59:12Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"e713861312306f0854012e6cade1703e96dca0676869628a961a9aff015308fc","abstract_canon_sha256":"9adca4418e25eb671a0da1a61bc564ac8f6d5e0ac403e1e22bff5e75ed4cc5ac"},"schema_version":"1.0"},"canonical_sha256":"a267f3485082c39820dfe3231185184ca3a07b2545fe65a40d1a4bcf087f3f5e","source":{"kind":"arxiv","id":"1509.01762","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01762","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01762v1","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01762","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"pith_short_12","alias_value":"UJT7GSCQQLBZ","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UJT7GSCQQLBZQIG7","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UJT7GSCQ","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UJT7GSCQQLBZQIG74MRRDBIYJS","target":"record","payload":{"canonical_record":{"source":{"id":"1509.01762","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-06T02:59:12Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"e713861312306f0854012e6cade1703e96dca0676869628a961a9aff015308fc","abstract_canon_sha256":"9adca4418e25eb671a0da1a61bc564ac8f6d5e0ac403e1e22bff5e75ed4cc5ac"},"schema_version":"1.0"},"canonical_sha256":"a267f3485082c39820dfe3231185184ca3a07b2545fe65a40d1a4bcf087f3f5e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:50.657846Z","signature_b64":"Wv78dY7/psStZH2MV943uRuSlB/tBU4lSvuQjCl+mCPJhWFuTrjARBowEc+yPTlMSaSOoaLOkqBId9fKOuVaDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a267f3485082c39820dfe3231185184ca3a07b2545fe65a40d1a4bcf087f3f5e","last_reissued_at":"2026-05-18T01:33:50.657351Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:50.657351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.01762","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":"2026-05-18T01:33:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t0Xfvq3BOlzOUTWoUIcCZxFTxiaJEXro0J5nOH0VuJlcwtRqA9GWZMYagw0Jp4KxPZd2lKy57BhFuEa6E2pMDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T04:09:58.549408Z"},"content_sha256":"f11ab068b9b56a5f1f14ec66bef95cc107362a3453175b73d12e64674c538cd3","schema_version":"1.0","event_id":"sha256:f11ab068b9b56a5f1f14ec66bef95cc107362a3453175b73d12e64674c538cd3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UJT7GSCQQLBZQIG74MRRDBIYJS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial decay to equilibrium for the Becker-D\\\"oring equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Robert L. Pego, Ryan W. Murray","submitted_at":"2015-09-06T02:59:12Z","abstract_excerpt":"This paper studies rates of decay to equilibrium for the Becker-D\\\"oring equations with subcritical initial data. In particular, polynomial rates of decay are established when initial perturbations of equilibrium have polynomial moments. This is proved by using new dissipation estimates in polynomially weighted $\\ell^1$ spaces, operator decomposition techniques from kinetic theory, and interpolation estimates from the study of travelling waves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01762","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":"2026-05-18T01:33:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hkhBQ0uimghxNoZMsrG04IVAaET894FZ4bsF3pMZXNeHEdrh5uKqVF5L7Iy8BQ0n4TYyrwOV3nT3p5+5DoXRDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T04:09:58.550039Z"},"content_sha256":"d479757a522befaaeebaf89d9bf2bb6accfc36b90d3f16e8d23ef6a40a18624d","schema_version":"1.0","event_id":"sha256:d479757a522befaaeebaf89d9bf2bb6accfc36b90d3f16e8d23ef6a40a18624d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UJT7GSCQQLBZQIG74MRRDBIYJS/bundle.json","state_url":"https://pith.science/pith/UJT7GSCQQLBZQIG74MRRDBIYJS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UJT7GSCQQLBZQIG74MRRDBIYJS/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":"2026-06-06T04:09:58Z","links":{"resolver":"https://pith.science/pith/UJT7GSCQQLBZQIG74MRRDBIYJS","bundle":"https://pith.science/pith/UJT7GSCQQLBZQIG74MRRDBIYJS/bundle.json","state":"https://pith.science/pith/UJT7GSCQQLBZQIG74MRRDBIYJS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UJT7GSCQQLBZQIG74MRRDBIYJS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UJT7GSCQQLBZQIG74MRRDBIYJS","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":"9adca4418e25eb671a0da1a61bc564ac8f6d5e0ac403e1e22bff5e75ed4cc5ac","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-06T02:59:12Z","title_canon_sha256":"e713861312306f0854012e6cade1703e96dca0676869628a961a9aff015308fc"},"schema_version":"1.0","source":{"id":"1509.01762","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01762","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01762v1","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01762","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"pith_short_12","alias_value":"UJT7GSCQQLBZ","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UJT7GSCQQLBZQIG7","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UJT7GSCQ","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:d479757a522befaaeebaf89d9bf2bb6accfc36b90d3f16e8d23ef6a40a18624d","target":"graph","created_at":"2026-05-18T01:33:50Z","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":"This paper studies rates of decay to equilibrium for the Becker-D\\\"oring equations with subcritical initial data. In particular, polynomial rates of decay are established when initial perturbations of equilibrium have polynomial moments. This is proved by using new dissipation estimates in polynomially weighted $\\ell^1$ spaces, operator decomposition techniques from kinetic theory, and interpolation estimates from the study of travelling waves.","authors_text":"Robert L. Pego, Ryan W. Murray","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-06T02:59:12Z","title":"Polynomial decay to equilibrium for the Becker-D\\\"oring equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01762","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:f11ab068b9b56a5f1f14ec66bef95cc107362a3453175b73d12e64674c538cd3","target":"record","created_at":"2026-05-18T01:33:50Z","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":"9adca4418e25eb671a0da1a61bc564ac8f6d5e0ac403e1e22bff5e75ed4cc5ac","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-06T02:59:12Z","title_canon_sha256":"e713861312306f0854012e6cade1703e96dca0676869628a961a9aff015308fc"},"schema_version":"1.0","source":{"id":"1509.01762","kind":"arxiv","version":1}},"canonical_sha256":"a267f3485082c39820dfe3231185184ca3a07b2545fe65a40d1a4bcf087f3f5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a267f3485082c39820dfe3231185184ca3a07b2545fe65a40d1a4bcf087f3f5e","first_computed_at":"2026-05-18T01:33:50.657351Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:50.657351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wv78dY7/psStZH2MV943uRuSlB/tBU4lSvuQjCl+mCPJhWFuTrjARBowEc+yPTlMSaSOoaLOkqBId9fKOuVaDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:50.657846Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.01762","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f11ab068b9b56a5f1f14ec66bef95cc107362a3453175b73d12e64674c538cd3","sha256:d479757a522befaaeebaf89d9bf2bb6accfc36b90d3f16e8d23ef6a40a18624d"],"state_sha256":"55e17b8e4a5cd9b6055211f86bd13a577faf432d1c427f05d27830bed6eca88c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"937/EBe7ELhGDIYnnp0KiPxXXom/hLfVOdmBpVQ0fVpytHryuexbm6zWunjCqWCiC1SOvTcQmz/jJ4m3wH5eAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T04:09:58.553394Z","bundle_sha256":"c9f1456b5939187ba6250da7f5edade319e3ba9f201544bfb4321a735e6746f3"}}