{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:EEFDPCTAXBQWUYGQZALVIN76J2","short_pith_number":"pith:EEFDPCTA","canonical_record":{"source":{"id":"1409.4611","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-09-16T12:45:28Z","cross_cats_sorted":[],"title_canon_sha256":"1ff9ddfc55447927fb62399522a98c81f6d9f27b508ee3b9030a1df27fb6d810","abstract_canon_sha256":"4365fbf488a6bb63cc5378da1bf9b85da2f5e599fcd8eb77d306a9f5b621889b"},"schema_version":"1.0"},"canonical_sha256":"210a378a60b8616a60d0c8175437fe4e8e8a46a658d6e86f0787de951acbdcbf","source":{"kind":"arxiv","id":"1409.4611","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.4611","created_at":"2026-05-18T02:20:39Z"},{"alias_kind":"arxiv_version","alias_value":"1409.4611v2","created_at":"2026-05-18T02:20:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4611","created_at":"2026-05-18T02:20:39Z"},{"alias_kind":"pith_short_12","alias_value":"EEFDPCTAXBQW","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EEFDPCTAXBQWUYGQ","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EEFDPCTA","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:EEFDPCTAXBQWUYGQZALVIN76J2","target":"record","payload":{"canonical_record":{"source":{"id":"1409.4611","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-09-16T12:45:28Z","cross_cats_sorted":[],"title_canon_sha256":"1ff9ddfc55447927fb62399522a98c81f6d9f27b508ee3b9030a1df27fb6d810","abstract_canon_sha256":"4365fbf488a6bb63cc5378da1bf9b85da2f5e599fcd8eb77d306a9f5b621889b"},"schema_version":"1.0"},"canonical_sha256":"210a378a60b8616a60d0c8175437fe4e8e8a46a658d6e86f0787de951acbdcbf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:39.971645Z","signature_b64":"Noxu8AXuUe/un8iFTLwkjPlrdNkAvhp2CKcl1S6JAi8yO8MTwTVSyrRoixwT1Dl91IRdOMmUB6i5WRuYlGwzAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"210a378a60b8616a60d0c8175437fe4e8e8a46a658d6e86f0787de951acbdcbf","last_reissued_at":"2026-05-18T02:20:39.970983Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:39.970983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.4611","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":"2026-05-18T02:20:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g5qJbufsqFUWdKTBHWXJE8N4MDDjRFHD5Xhyobvw5aWX8z9IjoCaDwQw9dUL3gK50x3VWW0Hj8TIK4BKX029Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:22:54.689921Z"},"content_sha256":"c28df0c37005ca9b0ec213ca6a0c16fc9e186252f1eaee93ef0478f1a4dd43f4","schema_version":"1.0","event_id":"sha256:c28df0c37005ca9b0ec213ca6a0c16fc9e186252f1eaee93ef0478f1a4dd43f4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:EEFDPCTAXBQWUYGQZALVIN76J2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On multi-scale percolation behaviour of the effective conductivity for the lattice model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"D. Fr\\k{a}czek, R. Piasecki, R. Wi\\'sniowski, W. Olchawa","submitted_at":"2014-09-16T12:45:28Z","abstract_excerpt":"Macroscopic properties of heterogeneous media are frequently modelled by regular lattice models, which are based on a relatively small basic cluster of lattice sites. Here, we extend one of such models to any cluster's size kxk. We also explore its modified form. The focus is on the percolation behaviour of the effective conductivity of random two- and three-phase systems. We consider only the influence of geometrical features of local configurations at different length scales k. At scales accessible numerically, we find that an increase in the size of the basic cluster leads to characteristic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4611","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":"2026-05-18T02:20:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JIBpClb8BV3jttY5l5qVH25WJzf4KUehl9he1gx1f0Q7NM+eUnxZDh3nN0qj9vlqit5Gxj0VVHwO/aU5zNjpBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:22:54.690261Z"},"content_sha256":"8a716b29924bc561f6bc431b65faf95949ed63133df098e1dd0e8517756ab8eb","schema_version":"1.0","event_id":"sha256:8a716b29924bc561f6bc431b65faf95949ed63133df098e1dd0e8517756ab8eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EEFDPCTAXBQWUYGQZALVIN76J2/bundle.json","state_url":"https://pith.science/pith/EEFDPCTAXBQWUYGQZALVIN76J2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EEFDPCTAXBQWUYGQZALVIN76J2/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":"2026-06-24T22:22:54Z","links":{"resolver":"https://pith.science/pith/EEFDPCTAXBQWUYGQZALVIN76J2","bundle":"https://pith.science/pith/EEFDPCTAXBQWUYGQZALVIN76J2/bundle.json","state":"https://pith.science/pith/EEFDPCTAXBQWUYGQZALVIN76J2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EEFDPCTAXBQWUYGQZALVIN76J2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EEFDPCTAXBQWUYGQZALVIN76J2","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":"4365fbf488a6bb63cc5378da1bf9b85da2f5e599fcd8eb77d306a9f5b621889b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-09-16T12:45:28Z","title_canon_sha256":"1ff9ddfc55447927fb62399522a98c81f6d9f27b508ee3b9030a1df27fb6d810"},"schema_version":"1.0","source":{"id":"1409.4611","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.4611","created_at":"2026-05-18T02:20:39Z"},{"alias_kind":"arxiv_version","alias_value":"1409.4611v2","created_at":"2026-05-18T02:20:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4611","created_at":"2026-05-18T02:20:39Z"},{"alias_kind":"pith_short_12","alias_value":"EEFDPCTAXBQW","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EEFDPCTAXBQWUYGQ","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EEFDPCTA","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:8a716b29924bc561f6bc431b65faf95949ed63133df098e1dd0e8517756ab8eb","target":"graph","created_at":"2026-05-18T02:20:39Z","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":"Macroscopic properties of heterogeneous media are frequently modelled by regular lattice models, which are based on a relatively small basic cluster of lattice sites. Here, we extend one of such models to any cluster's size kxk. We also explore its modified form. The focus is on the percolation behaviour of the effective conductivity of random two- and three-phase systems. We consider only the influence of geometrical features of local configurations at different length scales k. At scales accessible numerically, we find that an increase in the size of the basic cluster leads to characteristic","authors_text":"D. Fr\\k{a}czek, R. Piasecki, R. Wi\\'sniowski, W. Olchawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-09-16T12:45:28Z","title":"On multi-scale percolation behaviour of the effective conductivity for the lattice model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4611","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:c28df0c37005ca9b0ec213ca6a0c16fc9e186252f1eaee93ef0478f1a4dd43f4","target":"record","created_at":"2026-05-18T02:20:39Z","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":"4365fbf488a6bb63cc5378da1bf9b85da2f5e599fcd8eb77d306a9f5b621889b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-09-16T12:45:28Z","title_canon_sha256":"1ff9ddfc55447927fb62399522a98c81f6d9f27b508ee3b9030a1df27fb6d810"},"schema_version":"1.0","source":{"id":"1409.4611","kind":"arxiv","version":2}},"canonical_sha256":"210a378a60b8616a60d0c8175437fe4e8e8a46a658d6e86f0787de951acbdcbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"210a378a60b8616a60d0c8175437fe4e8e8a46a658d6e86f0787de951acbdcbf","first_computed_at":"2026-05-18T02:20:39.970983Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:39.970983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Noxu8AXuUe/un8iFTLwkjPlrdNkAvhp2CKcl1S6JAi8yO8MTwTVSyrRoixwT1Dl91IRdOMmUB6i5WRuYlGwzAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:39.971645Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.4611","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c28df0c37005ca9b0ec213ca6a0c16fc9e186252f1eaee93ef0478f1a4dd43f4","sha256:8a716b29924bc561f6bc431b65faf95949ed63133df098e1dd0e8517756ab8eb"],"state_sha256":"4691d8027147083dbefe82768d462a26a5bce3b213d63f4a20b73bfaca8800b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"osRzEaR8zZ0GHBwRH8eWdfEmb5o9VEbceZZmZ3T0Lj4ZCxdIUNbYQCgjRYFKcLITtDnVrIrzlMJgcX1UBmg1CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T22:22:54.692292Z","bundle_sha256":"ccf813a97e57a33e7fea8b5d05f52d47e623440ccab6102b34029b1f488dc14a"}}