{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:IPDS3SDGJPLJ2WF7LRYSSGE2KS","short_pith_number":"pith:IPDS3SDG","canonical_record":{"source":{"id":"cond-mat/0008334","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2000-08-23T16:09:12Z","cross_cats_sorted":[],"title_canon_sha256":"cf83e371477356e795c5185db953b48caa21fdab0f20b905848e6735267bc57e","abstract_canon_sha256":"ec35abb43ecdb980e7bdc018d8976314d8c1cff32152b0726cb5633d5779d3db"},"schema_version":"1.0"},"canonical_sha256":"43c72dc8664bd69d58bf5c7129189a54ab38b9e3e995813cb6fcb7a12607dfa5","source":{"kind":"arxiv","id":"cond-mat/0008334","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0008334","created_at":"2026-05-18T00:34:17Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0008334v1","created_at":"2026-05-18T00:34:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0008334","created_at":"2026-05-18T00:34:17Z"},{"alias_kind":"pith_short_12","alias_value":"IPDS3SDGJPLJ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"IPDS3SDGJPLJ2WF7","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"IPDS3SDG","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:IPDS3SDGJPLJ2WF7LRYSSGE2KS","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0008334","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2000-08-23T16:09:12Z","cross_cats_sorted":[],"title_canon_sha256":"cf83e371477356e795c5185db953b48caa21fdab0f20b905848e6735267bc57e","abstract_canon_sha256":"ec35abb43ecdb980e7bdc018d8976314d8c1cff32152b0726cb5633d5779d3db"},"schema_version":"1.0"},"canonical_sha256":"43c72dc8664bd69d58bf5c7129189a54ab38b9e3e995813cb6fcb7a12607dfa5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:17.154777Z","signature_b64":"f8YU0y4bQyxCHQVQSrnfddgGNrlMuyTEA0/8Rvg3/in9vq0IKJBfdcCYYQvYygx5W+muowJSkPkyv2LyYwlsCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43c72dc8664bd69d58bf5c7129189a54ab38b9e3e995813cb6fcb7a12607dfa5","last_reissued_at":"2026-05-18T00:34:17.154049Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:17.154049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0008334","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":"2026-05-18T00:34:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ihiU0Ny0+ajFYtnKUNwD5ahNOq9OHgsGVfY8GgDIrfCAWC26KehKzU//uVFEBPPDw+hQNPkuTxSGNp/w/5ERAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T16:08:10.452142Z"},"content_sha256":"787791b9781e590532c4783671cca951986670c7a83a5bdc247b233de1b48e0e","schema_version":"1.0","event_id":"sha256:787791b9781e590532c4783671cca951986670c7a83a5bdc247b233de1b48e0e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:IPDS3SDGJPLJ2WF7LRYSSGE2KS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coarsened Lattice Spatial Disorder in the Thermodynamic Limit","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"A. Czainski, R. Piasecki","submitted_at":"2000-08-23T16:09:12Z","abstract_excerpt":"In this Rapid Research Note the application of recently introduced [Physica A 277 (2000) 157] entropic measure S_Delta of spatial disorder for systems of finite-sized objects is presented. In the thermodynamic limit the critical behaviour of coarsened lattice model of random two-phase systems is illustrated for certain grain size distributions (GSDs) and chosen parameters. Also the changes of spatial disorder, quantified by S_Delta, between the limit GSDs clearly show that the topological equivalence of the two phases is broken."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0008334","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":"2026-05-18T00:34:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eF1QTKnX/wLTPwzp+4vqhnw2THmgYNbFQhIC3hz4Sz1oPgbu89oqfAga/6sA9ZtalvgKYnB4VVpN0JhIIn3GDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T16:08:10.452510Z"},"content_sha256":"d942fe80c837d0498dfb16d9fe28bfd441cdf9fdc3cde29a3ebb9f7bb07393b4","schema_version":"1.0","event_id":"sha256:d942fe80c837d0498dfb16d9fe28bfd441cdf9fdc3cde29a3ebb9f7bb07393b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IPDS3SDGJPLJ2WF7LRYSSGE2KS/bundle.json","state_url":"https://pith.science/pith/IPDS3SDGJPLJ2WF7LRYSSGE2KS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IPDS3SDGJPLJ2WF7LRYSSGE2KS/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":"2026-06-24T16:08:10Z","links":{"resolver":"https://pith.science/pith/IPDS3SDGJPLJ2WF7LRYSSGE2KS","bundle":"https://pith.science/pith/IPDS3SDGJPLJ2WF7LRYSSGE2KS/bundle.json","state":"https://pith.science/pith/IPDS3SDGJPLJ2WF7LRYSSGE2KS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IPDS3SDGJPLJ2WF7LRYSSGE2KS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:IPDS3SDGJPLJ2WF7LRYSSGE2KS","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":"ec35abb43ecdb980e7bdc018d8976314d8c1cff32152b0726cb5633d5779d3db","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2000-08-23T16:09:12Z","title_canon_sha256":"cf83e371477356e795c5185db953b48caa21fdab0f20b905848e6735267bc57e"},"schema_version":"1.0","source":{"id":"cond-mat/0008334","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0008334","created_at":"2026-05-18T00:34:17Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0008334v1","created_at":"2026-05-18T00:34:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0008334","created_at":"2026-05-18T00:34:17Z"},{"alias_kind":"pith_short_12","alias_value":"IPDS3SDGJPLJ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"IPDS3SDGJPLJ2WF7","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"IPDS3SDG","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:d942fe80c837d0498dfb16d9fe28bfd441cdf9fdc3cde29a3ebb9f7bb07393b4","target":"graph","created_at":"2026-05-18T00:34:17Z","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":"In this Rapid Research Note the application of recently introduced [Physica A 277 (2000) 157] entropic measure S_Delta of spatial disorder for systems of finite-sized objects is presented. In the thermodynamic limit the critical behaviour of coarsened lattice model of random two-phase systems is illustrated for certain grain size distributions (GSDs) and chosen parameters. Also the changes of spatial disorder, quantified by S_Delta, between the limit GSDs clearly show that the topological equivalence of the two phases is broken.","authors_text":"A. Czainski, R. Piasecki","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2000-08-23T16:09:12Z","title":"Coarsened Lattice Spatial Disorder in the Thermodynamic Limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0008334","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":"sha256:787791b9781e590532c4783671cca951986670c7a83a5bdc247b233de1b48e0e","target":"record","created_at":"2026-05-18T00:34:17Z","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":"ec35abb43ecdb980e7bdc018d8976314d8c1cff32152b0726cb5633d5779d3db","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2000-08-23T16:09:12Z","title_canon_sha256":"cf83e371477356e795c5185db953b48caa21fdab0f20b905848e6735267bc57e"},"schema_version":"1.0","source":{"id":"cond-mat/0008334","kind":"arxiv","version":1}},"canonical_sha256":"43c72dc8664bd69d58bf5c7129189a54ab38b9e3e995813cb6fcb7a12607dfa5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43c72dc8664bd69d58bf5c7129189a54ab38b9e3e995813cb6fcb7a12607dfa5","first_computed_at":"2026-05-18T00:34:17.154049Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:17.154049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f8YU0y4bQyxCHQVQSrnfddgGNrlMuyTEA0/8Rvg3/in9vq0IKJBfdcCYYQvYygx5W+muowJSkPkyv2LyYwlsCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:17.154777Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0008334","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:787791b9781e590532c4783671cca951986670c7a83a5bdc247b233de1b48e0e","sha256:d942fe80c837d0498dfb16d9fe28bfd441cdf9fdc3cde29a3ebb9f7bb07393b4"],"state_sha256":"5a29eddf2546352224f6cff58d8654744a5336d6b787a834882df8d302c63fb1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/K3nEgX+A+mmqFq/RgdTafNta5PXwkhheE0Av0yGxtv8wJ2IxaGiwQu+A5UynPYkG+U4EOE+wa309dpqVhW4Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T16:08:10.454467Z","bundle_sha256":"31569d569f5c3d946911ce730cc5d8a666631fe12ab60dd3842eb11d012e38cb"}}