{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:55CNG4EJ3MYAK3IIHZ6ML3QTSQ","short_pith_number":"pith:55CNG4EJ","canonical_record":{"source":{"id":"1405.2453","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2014-05-10T16:58:58Z","cross_cats_sorted":[],"title_canon_sha256":"89581e0960eb6667b77a8fc6e90aeefdac384d9c43632bb9796154acf05b7713","abstract_canon_sha256":"87cd05bc4e8d4af3cfb98c35858b740de0367cd023fc8b27783e6cbd114a6a14"},"schema_version":"1.0"},"canonical_sha256":"ef44d37089db30056d083e7cc5ee1394263c5836d37d5bf93f534df903f76958","source":{"kind":"arxiv","id":"1405.2453","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2453","created_at":"2026-05-18T02:51:07Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2453v1","created_at":"2026-05-18T02:51:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2453","created_at":"2026-05-18T02:51:07Z"},{"alias_kind":"pith_short_12","alias_value":"55CNG4EJ3MYA","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"55CNG4EJ3MYAK3II","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"55CNG4EJ","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:55CNG4EJ3MYAK3IIHZ6ML3QTSQ","target":"record","payload":{"canonical_record":{"source":{"id":"1405.2453","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2014-05-10T16:58:58Z","cross_cats_sorted":[],"title_canon_sha256":"89581e0960eb6667b77a8fc6e90aeefdac384d9c43632bb9796154acf05b7713","abstract_canon_sha256":"87cd05bc4e8d4af3cfb98c35858b740de0367cd023fc8b27783e6cbd114a6a14"},"schema_version":"1.0"},"canonical_sha256":"ef44d37089db30056d083e7cc5ee1394263c5836d37d5bf93f534df903f76958","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:07.893657Z","signature_b64":"aRCU7FXgjg49WXQUx/Yh8W/9xDKX+tXjUNssZsUwbRrxr443P4ZTh8RdFBgmFsLgMGfC7nodC4VSPHKM0Oj+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef44d37089db30056d083e7cc5ee1394263c5836d37d5bf93f534df903f76958","last_reissued_at":"2026-05-18T02:51:07.893216Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:07.893216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.2453","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":"2026-05-18T02:51:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yv626GHpzYkzJfyfwDLbpbj0upFH6v/ViiQNxWy5oTTi5nRunNZufDIldRQeUC5MYCM/mret5o5kdN+zRLUsCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:24:56.340118Z"},"content_sha256":"019ff4a06e24ddcdd349246eb051581975bf99c1adbc8b31e5d0339bd0b06b78","schema_version":"1.0","event_id":"sha256:019ff4a06e24ddcdd349246eb051581975bf99c1adbc8b31e5d0339bd0b06b78"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:55CNG4EJ3MYAK3IIHZ6ML3QTSQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Statistical theory of correlations in random packings of hard particles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.soft","authors_text":"Hernan A. Makse, James G. Puckett, Yuliang Jin","submitted_at":"2014-05-10T16:58:58Z","abstract_excerpt":"A random packing of hard particles represents a fundamental model for granular matter. Despite its importance, analytical modeling of random packings remains difficult due to the existence of strong correlations which preclude the development of a simple theory. Here, we take inspiration from liquid theories for the $n$-particle angular correlation function to develop a formalism of random packings of hard particles from the bottom-up. A progressive expansion into a shell of particles converges in the large layer limit under a Kirkwood-like approximation of higher-order correlations. We apply "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2453","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":"2026-05-18T02:51:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"blLu+y66cfzmOcjGcq4X58+Cb33RSWsV1AidNUvzj31yX/ZS5B/kJ9POJaWn/ptKPpch9o4B5BaDrmT8J+gYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:24:56.340938Z"},"content_sha256":"5c9ae2c871baa499742f25f99bdefd9c7b438d5e3e78c1b62a03e1eb2cd0ad8f","schema_version":"1.0","event_id":"sha256:5c9ae2c871baa499742f25f99bdefd9c7b438d5e3e78c1b62a03e1eb2cd0ad8f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/55CNG4EJ3MYAK3IIHZ6ML3QTSQ/bundle.json","state_url":"https://pith.science/pith/55CNG4EJ3MYAK3IIHZ6ML3QTSQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/55CNG4EJ3MYAK3IIHZ6ML3QTSQ/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":"2026-05-27T06:24:56Z","links":{"resolver":"https://pith.science/pith/55CNG4EJ3MYAK3IIHZ6ML3QTSQ","bundle":"https://pith.science/pith/55CNG4EJ3MYAK3IIHZ6ML3QTSQ/bundle.json","state":"https://pith.science/pith/55CNG4EJ3MYAK3IIHZ6ML3QTSQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/55CNG4EJ3MYAK3IIHZ6ML3QTSQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:55CNG4EJ3MYAK3IIHZ6ML3QTSQ","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":"87cd05bc4e8d4af3cfb98c35858b740de0367cd023fc8b27783e6cbd114a6a14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2014-05-10T16:58:58Z","title_canon_sha256":"89581e0960eb6667b77a8fc6e90aeefdac384d9c43632bb9796154acf05b7713"},"schema_version":"1.0","source":{"id":"1405.2453","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2453","created_at":"2026-05-18T02:51:07Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2453v1","created_at":"2026-05-18T02:51:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2453","created_at":"2026-05-18T02:51:07Z"},{"alias_kind":"pith_short_12","alias_value":"55CNG4EJ3MYA","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"55CNG4EJ3MYAK3II","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"55CNG4EJ","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:5c9ae2c871baa499742f25f99bdefd9c7b438d5e3e78c1b62a03e1eb2cd0ad8f","target":"graph","created_at":"2026-05-18T02:51:07Z","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":"A random packing of hard particles represents a fundamental model for granular matter. Despite its importance, analytical modeling of random packings remains difficult due to the existence of strong correlations which preclude the development of a simple theory. Here, we take inspiration from liquid theories for the $n$-particle angular correlation function to develop a formalism of random packings of hard particles from the bottom-up. A progressive expansion into a shell of particles converges in the large layer limit under a Kirkwood-like approximation of higher-order correlations. We apply ","authors_text":"Hernan A. Makse, James G. Puckett, Yuliang Jin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2014-05-10T16:58:58Z","title":"Statistical theory of correlations in random packings of hard particles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2453","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":"sha256:019ff4a06e24ddcdd349246eb051581975bf99c1adbc8b31e5d0339bd0b06b78","target":"record","created_at":"2026-05-18T02:51:07Z","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":"87cd05bc4e8d4af3cfb98c35858b740de0367cd023fc8b27783e6cbd114a6a14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2014-05-10T16:58:58Z","title_canon_sha256":"89581e0960eb6667b77a8fc6e90aeefdac384d9c43632bb9796154acf05b7713"},"schema_version":"1.0","source":{"id":"1405.2453","kind":"arxiv","version":1}},"canonical_sha256":"ef44d37089db30056d083e7cc5ee1394263c5836d37d5bf93f534df903f76958","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef44d37089db30056d083e7cc5ee1394263c5836d37d5bf93f534df903f76958","first_computed_at":"2026-05-18T02:51:07.893216Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:07.893216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aRCU7FXgjg49WXQUx/Yh8W/9xDKX+tXjUNssZsUwbRrxr443P4ZTh8RdFBgmFsLgMGfC7nodC4VSPHKM0Oj+Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:07.893657Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.2453","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:019ff4a06e24ddcdd349246eb051581975bf99c1adbc8b31e5d0339bd0b06b78","sha256:5c9ae2c871baa499742f25f99bdefd9c7b438d5e3e78c1b62a03e1eb2cd0ad8f"],"state_sha256":"045bc975e9ce0f8cb3dbdac90320f0559253047456fc2bd1fb8b9a4a6368538d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yf3xM1p9qUe1KgwV6sFhfPYjv3qVoKtQAZhvgJYxN1LTHPr4cnAjEgLdXljqAxl61aoq1Wd2UvJ0d9JOgk/0Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T06:24:56.343206Z","bundle_sha256":"ef6b505e5e8abe7751b430815846c86998203481caa7d4ff280bcc44e819a8b6"}}