{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7MM2CNMVXP5QMOEL4OHRAQTMZU","short_pith_number":"pith:7MM2CNMV","canonical_record":{"source":{"id":"1608.01984","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-08-05T19:43:26Z","cross_cats_sorted":["cond-mat.soft"],"title_canon_sha256":"eed7fd32601f48c6460ec8890807235bc648efb4c6384d44225584328c3e6952","abstract_canon_sha256":"43c7973ddd6f4ff8dd8ae208f9ff68638f822ee894f203989c12fa11275cdf5d"},"schema_version":"1.0"},"canonical_sha256":"fb19a13595bbfb06388be38f10426ccd36e05e3ddff6d450905731c11506449e","source":{"kind":"arxiv","id":"1608.01984","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01984","created_at":"2026-05-18T01:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01984v2","created_at":"2026-05-18T01:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01984","created_at":"2026-05-18T01:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"7MM2CNMVXP5Q","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7MM2CNMVXP5QMOEL","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7MM2CNMV","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7MM2CNMVXP5QMOEL4OHRAQTMZU","target":"record","payload":{"canonical_record":{"source":{"id":"1608.01984","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-08-05T19:43:26Z","cross_cats_sorted":["cond-mat.soft"],"title_canon_sha256":"eed7fd32601f48c6460ec8890807235bc648efb4c6384d44225584328c3e6952","abstract_canon_sha256":"43c7973ddd6f4ff8dd8ae208f9ff68638f822ee894f203989c12fa11275cdf5d"},"schema_version":"1.0"},"canonical_sha256":"fb19a13595bbfb06388be38f10426ccd36e05e3ddff6d450905731c11506449e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:42.967189Z","signature_b64":"IusudKGeSQeVlq1df8yvTgnfxBIiQfFtfoWTg1o0a1kFjMSpigejNQFz5xMO2EUgwzroFjuzwLOfcjYUuSfTDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb19a13595bbfb06388be38f10426ccd36e05e3ddff6d450905731c11506449e","last_reissued_at":"2026-05-18T01:04:42.966735Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:42.966735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.01984","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":"2026-05-18T01:04:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FVcTeILWhX8L/g9OAmYSY7oyo534SQCE8Dpn40S8jppDU2/VZapglViFq5sQuZcl6KwZFidwKyLfU2qKRAgkBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:12:40.075145Z"},"content_sha256":"63e491027a5092afe0d7b02903f9d737e534482925f26f29260712a8b744f4a4","schema_version":"1.0","event_id":"sha256:63e491027a5092afe0d7b02903f9d737e534482925f26f29260712a8b744f4a4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7MM2CNMVXP5QMOEL4OHRAQTMZU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterization of Maximally Random Jammed Sphere Packings: II. Correlation Functions and Density Fluctuations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft"],"primary_cat":"cond-mat.stat-mech","authors_text":"Michael A. Klatt, Salvatore Torquato","submitted_at":"2016-08-05T19:43:26Z","abstract_excerpt":"In the first paper of this series, we introduced Voronoi correlation functions to characterize the structure of maximally random jammed (MRJ) sphere packings across length scales. In the present paper, we determine a variety of correlation functions that can be rigorously related to effective physical properties of MRJ sphere packings and compare them to the corresponding statistical descriptors for overlapping spheres and equilibrium hard-sphere systems. Such structural descriptors arise in rigorous bounds and formulas for effective transport properties, diffusion and reactions constants, ela"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01984","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":"2026-05-18T01:04:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oC9yOZcsRTqNlmMAb4ryY/8TLNIDgSJ80a3XIQ2OuqxTmUq9f5KxFOVCcarEjcYem3Nn8mc3CjB/GZXpS9SQBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:12:40.075858Z"},"content_sha256":"becf4fc2e18eac25aea1695322b67dcd65ee5966dd88b274adeabf12b2e20101","schema_version":"1.0","event_id":"sha256:becf4fc2e18eac25aea1695322b67dcd65ee5966dd88b274adeabf12b2e20101"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7MM2CNMVXP5QMOEL4OHRAQTMZU/bundle.json","state_url":"https://pith.science/pith/7MM2CNMVXP5QMOEL4OHRAQTMZU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7MM2CNMVXP5QMOEL4OHRAQTMZU/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":"2026-05-31T05:12:40Z","links":{"resolver":"https://pith.science/pith/7MM2CNMVXP5QMOEL4OHRAQTMZU","bundle":"https://pith.science/pith/7MM2CNMVXP5QMOEL4OHRAQTMZU/bundle.json","state":"https://pith.science/pith/7MM2CNMVXP5QMOEL4OHRAQTMZU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7MM2CNMVXP5QMOEL4OHRAQTMZU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7MM2CNMVXP5QMOEL4OHRAQTMZU","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":"43c7973ddd6f4ff8dd8ae208f9ff68638f822ee894f203989c12fa11275cdf5d","cross_cats_sorted":["cond-mat.soft"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-08-05T19:43:26Z","title_canon_sha256":"eed7fd32601f48c6460ec8890807235bc648efb4c6384d44225584328c3e6952"},"schema_version":"1.0","source":{"id":"1608.01984","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01984","created_at":"2026-05-18T01:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01984v2","created_at":"2026-05-18T01:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01984","created_at":"2026-05-18T01:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"7MM2CNMVXP5Q","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7MM2CNMVXP5QMOEL","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7MM2CNMV","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:becf4fc2e18eac25aea1695322b67dcd65ee5966dd88b274adeabf12b2e20101","target":"graph","created_at":"2026-05-18T01:04:42Z","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 the first paper of this series, we introduced Voronoi correlation functions to characterize the structure of maximally random jammed (MRJ) sphere packings across length scales. In the present paper, we determine a variety of correlation functions that can be rigorously related to effective physical properties of MRJ sphere packings and compare them to the corresponding statistical descriptors for overlapping spheres and equilibrium hard-sphere systems. Such structural descriptors arise in rigorous bounds and formulas for effective transport properties, diffusion and reactions constants, ela","authors_text":"Michael A. Klatt, Salvatore Torquato","cross_cats":["cond-mat.soft"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-08-05T19:43:26Z","title":"Characterization of Maximally Random Jammed Sphere Packings: II. Correlation Functions and Density Fluctuations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01984","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":"sha256:63e491027a5092afe0d7b02903f9d737e534482925f26f29260712a8b744f4a4","target":"record","created_at":"2026-05-18T01:04:42Z","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":"43c7973ddd6f4ff8dd8ae208f9ff68638f822ee894f203989c12fa11275cdf5d","cross_cats_sorted":["cond-mat.soft"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-08-05T19:43:26Z","title_canon_sha256":"eed7fd32601f48c6460ec8890807235bc648efb4c6384d44225584328c3e6952"},"schema_version":"1.0","source":{"id":"1608.01984","kind":"arxiv","version":2}},"canonical_sha256":"fb19a13595bbfb06388be38f10426ccd36e05e3ddff6d450905731c11506449e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb19a13595bbfb06388be38f10426ccd36e05e3ddff6d450905731c11506449e","first_computed_at":"2026-05-18T01:04:42.966735Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:42.966735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IusudKGeSQeVlq1df8yvTgnfxBIiQfFtfoWTg1o0a1kFjMSpigejNQFz5xMO2EUgwzroFjuzwLOfcjYUuSfTDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:42.967189Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.01984","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63e491027a5092afe0d7b02903f9d737e534482925f26f29260712a8b744f4a4","sha256:becf4fc2e18eac25aea1695322b67dcd65ee5966dd88b274adeabf12b2e20101"],"state_sha256":"c7b619ea222eefb9c5bdafb57b43bc46a75fe3ba89056c138b904cf27aa51341"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NJaiZ6ZtiYzYGfE5yO2UxrIfZGoW+QzQXXD6Jf3X8zFcWZseDMcFOHVv4fpYFga2uKDrS6FwHb1Xq024JoBiDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:12:40.079621Z","bundle_sha256":"5b639fd2935433ad9309bcd5a2f8dc1521a9e267e8fed8ec00f2330411ef76ef"}}