{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7UGK52E5JK25EW6JIW3Z23ZWJK","short_pith_number":"pith:7UGK52E5","canonical_record":{"source":{"id":"1605.08984","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-29T09:38:08Z","cross_cats_sorted":[],"title_canon_sha256":"80caf252b3b001b2c920f2d0ab55d01f619d9fcb10f98b017f7d0d29f1b013a8","abstract_canon_sha256":"aa9a3a565546abc7c152ca40f1ec6244f13d1435bc007374ef5d927c0a5cf4e6"},"schema_version":"1.0"},"canonical_sha256":"fd0caee89d4ab5d25bc945b79d6f364a8b50f76bf0d775ebc5058ce26f53019a","source":{"kind":"arxiv","id":"1605.08984","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.08984","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"arxiv_version","alias_value":"1605.08984v1","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08984","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"pith_short_12","alias_value":"7UGK52E5JK25","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7UGK52E5JK25EW6J","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7UGK52E5","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7UGK52E5JK25EW6JIW3Z23ZWJK","target":"record","payload":{"canonical_record":{"source":{"id":"1605.08984","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-29T09:38:08Z","cross_cats_sorted":[],"title_canon_sha256":"80caf252b3b001b2c920f2d0ab55d01f619d9fcb10f98b017f7d0d29f1b013a8","abstract_canon_sha256":"aa9a3a565546abc7c152ca40f1ec6244f13d1435bc007374ef5d927c0a5cf4e6"},"schema_version":"1.0"},"canonical_sha256":"fd0caee89d4ab5d25bc945b79d6f364a8b50f76bf0d775ebc5058ce26f53019a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:31.567194Z","signature_b64":"RiJbtKd6uu/CP4P4G2h+S87fvaS5NUjOBkGjmpHpEQL1+DDXu4sosyEfEq6cSDszxEzLM9PYjeYSeGXozLuXBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd0caee89d4ab5d25bc945b79d6f364a8b50f76bf0d775ebc5058ce26f53019a","last_reissued_at":"2026-05-18T00:09:31.566545Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:31.566545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.08984","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":"2026-05-18T00:09:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2RD9i/YGV5rXJg4DF3knhTz9RZPKI4A6UholbOZntMW9Fsfu8DsMKJ7cQp9CTQHGiQnIJz7DKkP5IZJ+dEdhDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T14:22:07.984762Z"},"content_sha256":"b5b422699fe7447920dc62d12da41545303df856882815fdb23d7084282d08a2","schema_version":"1.0","event_id":"sha256:b5b422699fe7447920dc62d12da41545303df856882815fdb23d7084282d08a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7UGK52E5JK25EW6JIW3Z23ZWJK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasi steady state approximation of the small clusters in Becker-D\\\"oring equations leads to boundary conditions in the Lifshitz-Slyozov limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Erwan Hingant, Julien Deschamps, Romain Yvinec","submitted_at":"2016-05-29T09:38:08Z","abstract_excerpt":"This papers addresses the connection between two classical models of phase transition phenomena describing different stages of the growth of clusters. The Becker-D\\\"oring model (BD) describes discrete-sized clusters through an infinite set of ordinary differential equations. The Lifshitz-Slyozov equation (LS) is a transport partial differential equation on the continuous half-line $x\\in (0,+\\infty)$. We introduce a scaling parameter $\\varepsilon>0$, which accounts for the grid size of the state space in the BD model, and recover the LS model in the limit $\\varepsilon\\to 0$. The connection has "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08984","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":"2026-05-18T00:09:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hYcYl13gDNwsofzy/37Cb+6F4IKVsS9NTCrhSf1UShCrSlGDdiagHMwG0uCpJFB2Tz6rnGDt6bqwAU/qPEp3BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T14:22:07.985111Z"},"content_sha256":"e8f007330e4c156bc52557f90a30491dbc87b28b2a98c42b8acf4665bf416211","schema_version":"1.0","event_id":"sha256:e8f007330e4c156bc52557f90a30491dbc87b28b2a98c42b8acf4665bf416211"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7UGK52E5JK25EW6JIW3Z23ZWJK/bundle.json","state_url":"https://pith.science/pith/7UGK52E5JK25EW6JIW3Z23ZWJK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7UGK52E5JK25EW6JIW3Z23ZWJK/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":"2026-06-09T14:22:07Z","links":{"resolver":"https://pith.science/pith/7UGK52E5JK25EW6JIW3Z23ZWJK","bundle":"https://pith.science/pith/7UGK52E5JK25EW6JIW3Z23ZWJK/bundle.json","state":"https://pith.science/pith/7UGK52E5JK25EW6JIW3Z23ZWJK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7UGK52E5JK25EW6JIW3Z23ZWJK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7UGK52E5JK25EW6JIW3Z23ZWJK","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":"aa9a3a565546abc7c152ca40f1ec6244f13d1435bc007374ef5d927c0a5cf4e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-29T09:38:08Z","title_canon_sha256":"80caf252b3b001b2c920f2d0ab55d01f619d9fcb10f98b017f7d0d29f1b013a8"},"schema_version":"1.0","source":{"id":"1605.08984","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.08984","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"arxiv_version","alias_value":"1605.08984v1","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08984","created_at":"2026-05-18T00:09:31Z"},{"alias_kind":"pith_short_12","alias_value":"7UGK52E5JK25","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7UGK52E5JK25EW6J","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7UGK52E5","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:e8f007330e4c156bc52557f90a30491dbc87b28b2a98c42b8acf4665bf416211","target":"graph","created_at":"2026-05-18T00:09:31Z","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 papers addresses the connection between two classical models of phase transition phenomena describing different stages of the growth of clusters. The Becker-D\\\"oring model (BD) describes discrete-sized clusters through an infinite set of ordinary differential equations. The Lifshitz-Slyozov equation (LS) is a transport partial differential equation on the continuous half-line $x\\in (0,+\\infty)$. We introduce a scaling parameter $\\varepsilon>0$, which accounts for the grid size of the state space in the BD model, and recover the LS model in the limit $\\varepsilon\\to 0$. The connection has ","authors_text":"Erwan Hingant, Julien Deschamps, Romain Yvinec","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-29T09:38:08Z","title":"Quasi steady state approximation of the small clusters in Becker-D\\\"oring equations leads to boundary conditions in the Lifshitz-Slyozov limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08984","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:b5b422699fe7447920dc62d12da41545303df856882815fdb23d7084282d08a2","target":"record","created_at":"2026-05-18T00:09:31Z","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":"aa9a3a565546abc7c152ca40f1ec6244f13d1435bc007374ef5d927c0a5cf4e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-29T09:38:08Z","title_canon_sha256":"80caf252b3b001b2c920f2d0ab55d01f619d9fcb10f98b017f7d0d29f1b013a8"},"schema_version":"1.0","source":{"id":"1605.08984","kind":"arxiv","version":1}},"canonical_sha256":"fd0caee89d4ab5d25bc945b79d6f364a8b50f76bf0d775ebc5058ce26f53019a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd0caee89d4ab5d25bc945b79d6f364a8b50f76bf0d775ebc5058ce26f53019a","first_computed_at":"2026-05-18T00:09:31.566545Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:31.566545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RiJbtKd6uu/CP4P4G2h+S87fvaS5NUjOBkGjmpHpEQL1+DDXu4sosyEfEq6cSDszxEzLM9PYjeYSeGXozLuXBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:31.567194Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.08984","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5b422699fe7447920dc62d12da41545303df856882815fdb23d7084282d08a2","sha256:e8f007330e4c156bc52557f90a30491dbc87b28b2a98c42b8acf4665bf416211"],"state_sha256":"fd438b398ac475b23f0357a960499001fc028f71c9d1dac8ecaaac78cde35d53"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2YjsLSVAzIUhrIiAOVCkkJUiQ42ShFMNby8N2Fb/v/piLnZp37KXwq9DtpDB9kTOUwyrhJTnCjGDGqCoJq5RCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T14:22:07.987029Z","bundle_sha256":"2f2d906d58965fa6bcd6ad5b1a52956ee7528d22ec550b3edd68bc2b3ffc6e34"}}