{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:UO2WKREUMNWT4PV2BRDAICGQDM","short_pith_number":"pith:UO2WKREU","canonical_record":{"source":{"id":"0909.5054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-09-28T09:59:27Z","cross_cats_sorted":[],"title_canon_sha256":"9e5b80680e4f18ae45477fe596a01b83b6c16e146c258f450480a8afdcd296fd","abstract_canon_sha256":"a527245e3866da72904afa97822d5820be2560a8e69a158322ddb0b6c7e8ee7b"},"schema_version":"1.0"},"canonical_sha256":"a3b5654494636d3e3eba0c460408d01b11a9a354801718041b8576e9af5add9c","source":{"kind":"arxiv","id":"0909.5054","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.5054","created_at":"2026-05-18T02:11:37Z"},{"alias_kind":"arxiv_version","alias_value":"0909.5054v1","created_at":"2026-05-18T02:11:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.5054","created_at":"2026-05-18T02:11:37Z"},{"alias_kind":"pith_short_12","alias_value":"UO2WKREUMNWT","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"UO2WKREUMNWT4PV2","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"UO2WKREU","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:UO2WKREUMNWT4PV2BRDAICGQDM","target":"record","payload":{"canonical_record":{"source":{"id":"0909.5054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-09-28T09:59:27Z","cross_cats_sorted":[],"title_canon_sha256":"9e5b80680e4f18ae45477fe596a01b83b6c16e146c258f450480a8afdcd296fd","abstract_canon_sha256":"a527245e3866da72904afa97822d5820be2560a8e69a158322ddb0b6c7e8ee7b"},"schema_version":"1.0"},"canonical_sha256":"a3b5654494636d3e3eba0c460408d01b11a9a354801718041b8576e9af5add9c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:11:37.013451Z","signature_b64":"9WYTOXAzxsdaFe1+7JeKv/SLCXyhF9Kj5mCCtdTQqBFsTmvS4mBx3NbJwoKQtz1UTppb7qVQOMwxWMviCEvxCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3b5654494636d3e3eba0c460408d01b11a9a354801718041b8576e9af5add9c","last_reissued_at":"2026-05-18T02:11:37.012722Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:11:37.012722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0909.5054","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":"2026-05-18T02:11:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZfY3niEu63Bpcm/a/BpOlDoJIb4AJ0UQ6c1mfvxYE8QVXeqF9iJ/Goiqnmbi6tDowDdaF6809nXtSpg0uTX9BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:18:33.106308Z"},"content_sha256":"65ae1885a333ac2965e29a2d412aef57aa6ee4d5eec34ad85cf1a029fe289d22","schema_version":"1.0","event_id":"sha256:65ae1885a333ac2965e29a2d412aef57aa6ee4d5eec34ad85cf1a029fe289d22"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:UO2WKREUMNWT4PV2BRDAICGQDM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Condensation Transition in Polydisperse Hard Rods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"E. Trizac, I. Pagonabarraga, M.R. Evans, S.N. Majumdar","submitted_at":"2009-09-28T09:59:27Z","abstract_excerpt":"We study a mass transport model, where spherical particles diffusing on a ring can stochastically exchange volume $v$, with the constraint of a fixed total volume $V=\\sum_{i=1}^N v_i$, $N$ being the total number of particles. The particles, referred to as $p$-spheres, have a linear size that behaves as $v_i^{1/p}$ and our model thus represents a gas of polydisperse hard rods with variable diameters $v_i^{1/p}$. We show that our model admits a factorized steady state distribution which provides the size distribution that minimizes the free energy of a polydisperse hard rod system, under the con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.5054","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":"2026-05-18T02:11:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yzG5jr6PbCRlgskCsRyVlJYFEdKzmEUjyCS5UezE/+bkY+PQhiDZXqqphzwMvrw3t5E8XMrTtGRBQ81HiPtPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:18:33.106663Z"},"content_sha256":"8f02a566d85430f2d65da005875f354490b1afa17516c9ec2130722471ef1318","schema_version":"1.0","event_id":"sha256:8f02a566d85430f2d65da005875f354490b1afa17516c9ec2130722471ef1318"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UO2WKREUMNWT4PV2BRDAICGQDM/bundle.json","state_url":"https://pith.science/pith/UO2WKREUMNWT4PV2BRDAICGQDM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UO2WKREUMNWT4PV2BRDAICGQDM/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":"2026-05-31T03:18:33Z","links":{"resolver":"https://pith.science/pith/UO2WKREUMNWT4PV2BRDAICGQDM","bundle":"https://pith.science/pith/UO2WKREUMNWT4PV2BRDAICGQDM/bundle.json","state":"https://pith.science/pith/UO2WKREUMNWT4PV2BRDAICGQDM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UO2WKREUMNWT4PV2BRDAICGQDM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:UO2WKREUMNWT4PV2BRDAICGQDM","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":"a527245e3866da72904afa97822d5820be2560a8e69a158322ddb0b6c7e8ee7b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-09-28T09:59:27Z","title_canon_sha256":"9e5b80680e4f18ae45477fe596a01b83b6c16e146c258f450480a8afdcd296fd"},"schema_version":"1.0","source":{"id":"0909.5054","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.5054","created_at":"2026-05-18T02:11:37Z"},{"alias_kind":"arxiv_version","alias_value":"0909.5054v1","created_at":"2026-05-18T02:11:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.5054","created_at":"2026-05-18T02:11:37Z"},{"alias_kind":"pith_short_12","alias_value":"UO2WKREUMNWT","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"UO2WKREUMNWT4PV2","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"UO2WKREU","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:8f02a566d85430f2d65da005875f354490b1afa17516c9ec2130722471ef1318","target":"graph","created_at":"2026-05-18T02:11:37Z","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 study a mass transport model, where spherical particles diffusing on a ring can stochastically exchange volume $v$, with the constraint of a fixed total volume $V=\\sum_{i=1}^N v_i$, $N$ being the total number of particles. The particles, referred to as $p$-spheres, have a linear size that behaves as $v_i^{1/p}$ and our model thus represents a gas of polydisperse hard rods with variable diameters $v_i^{1/p}$. We show that our model admits a factorized steady state distribution which provides the size distribution that minimizes the free energy of a polydisperse hard rod system, under the con","authors_text":"E. Trizac, I. Pagonabarraga, M.R. Evans, S.N. Majumdar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-09-28T09:59:27Z","title":"Condensation Transition in Polydisperse Hard Rods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.5054","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":"sha256:65ae1885a333ac2965e29a2d412aef57aa6ee4d5eec34ad85cf1a029fe289d22","target":"record","created_at":"2026-05-18T02:11:37Z","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":"a527245e3866da72904afa97822d5820be2560a8e69a158322ddb0b6c7e8ee7b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-09-28T09:59:27Z","title_canon_sha256":"9e5b80680e4f18ae45477fe596a01b83b6c16e146c258f450480a8afdcd296fd"},"schema_version":"1.0","source":{"id":"0909.5054","kind":"arxiv","version":1}},"canonical_sha256":"a3b5654494636d3e3eba0c460408d01b11a9a354801718041b8576e9af5add9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3b5654494636d3e3eba0c460408d01b11a9a354801718041b8576e9af5add9c","first_computed_at":"2026-05-18T02:11:37.012722Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:11:37.012722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9WYTOXAzxsdaFe1+7JeKv/SLCXyhF9Kj5mCCtdTQqBFsTmvS4mBx3NbJwoKQtz1UTppb7qVQOMwxWMviCEvxCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:11:37.013451Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.5054","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65ae1885a333ac2965e29a2d412aef57aa6ee4d5eec34ad85cf1a029fe289d22","sha256:8f02a566d85430f2d65da005875f354490b1afa17516c9ec2130722471ef1318"],"state_sha256":"58d2355a2ad1376e75cfc92d5f46eb874e63a8f1527b370137073f586b438c57"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x0DiQK2Wl6tJjTRvZv7koZU9/dW0dso0bDLfrgN1/FQW42oyOpD/6OBHf491wHyZu08SGFmtj/SasgS7alAXAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T03:18:33.108513Z","bundle_sha256":"197d52e18d47c0cf7b3310ee6f40737d2fff11ae669b8cc6fba4a6b5d7aa7897"}}