{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TQ3OEU4RJCXKL4TXJ5GFQ3QBSJ","short_pith_number":"pith:TQ3OEU4R","canonical_record":{"source":{"id":"1608.03347","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-08-11T02:06:50Z","cross_cats_sorted":["cond-mat.soft"],"title_canon_sha256":"800fa36a2c42156ec186888205b929f49bf88f9855c44cfaaceae806d5f4c924","abstract_canon_sha256":"e3d4555bdfc817382252f8f278b9b1d8d2fd657e01b8d3776b925e895b2d1c51"},"schema_version":"1.0"},"canonical_sha256":"9c36e2539148aea5f2774f4c586e01925550bfacc35d595f0c12743c8df08c2e","source":{"kind":"arxiv","id":"1608.03347","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03347","created_at":"2026-05-18T01:04:17Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03347v1","created_at":"2026-05-18T01:04:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03347","created_at":"2026-05-18T01:04:17Z"},{"alias_kind":"pith_short_12","alias_value":"TQ3OEU4RJCXK","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TQ3OEU4RJCXKL4TX","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TQ3OEU4R","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TQ3OEU4RJCXKL4TXJ5GFQ3QBSJ","target":"record","payload":{"canonical_record":{"source":{"id":"1608.03347","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-08-11T02:06:50Z","cross_cats_sorted":["cond-mat.soft"],"title_canon_sha256":"800fa36a2c42156ec186888205b929f49bf88f9855c44cfaaceae806d5f4c924","abstract_canon_sha256":"e3d4555bdfc817382252f8f278b9b1d8d2fd657e01b8d3776b925e895b2d1c51"},"schema_version":"1.0"},"canonical_sha256":"9c36e2539148aea5f2774f4c586e01925550bfacc35d595f0c12743c8df08c2e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:17.806358Z","signature_b64":"0waYv120nyLHueEywVUBXW1jwj1N8Plb0TtzCJp05IdUPQ0Ko0UkfwSzig5vztITuWqGcwm1K2OMTry1ReyaAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c36e2539148aea5f2774f4c586e01925550bfacc35d595f0c12743c8df08c2e","last_reissued_at":"2026-05-18T01:04:17.805842Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:17.805842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.03347","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":"2026-05-18T01:04:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dUDXWcWWHmnBE7zPofDinthLImOvZ8PYLiXEskzf2DMYDtPC05p2XaA/HsfMvOI2AFa2rDMg9Eyn19aZ48CUDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:13:20.016504Z"},"content_sha256":"432fd09e60a42fd3419bb6b74437e42f90feda5f82589055ead0565f064d4da1","schema_version":"1.0","event_id":"sha256:432fd09e60a42fd3419bb6b74437e42f90feda5f82589055ead0565f064d4da1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TQ3OEU4RJCXKL4TXJ5GFQ3QBSJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Static Structural Signatures of Nearly Jammed Disordered and Ordered Hard-Sphere Packings: Direct Correlation Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft"],"primary_cat":"cond-mat.stat-mech","authors_text":"Frank H. Stillinger, Salvatore Torquato, Steven Atkinson","submitted_at":"2016-08-11T02:06:50Z","abstract_excerpt":"Dynamical signatures are known to precede jamming in hard-particle systems, but static structural signatures have proven more elusive. The observation that compressing hard-particle packings towards jamming causes growing hyperuniformity has paved the way for the analysis of jamming as an \"inverted critical point\" in which the direct correlation function $c(r)$ diverges. We establish quantitative relationships between various singularities in $c(r)$ and the total correlation function $h(r)$ that provide a concrete means of identifying features that must be expressed in $c(r)$ if one hopes to r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03347","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":"2026-05-18T01:04:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bo+1QZhz8Liiq4zVV2Wbo4IDR3STi++/px/y1Ypaq6WEH2MNlyenNd9BnqJk9jEi0yNeJQBEWLkSxh6o+ch9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:13:20.019451Z"},"content_sha256":"2b27e24eefdf8a96348dabddc3468c4f2ddcd84e3d503b24098ec9691465eb3e","schema_version":"1.0","event_id":"sha256:2b27e24eefdf8a96348dabddc3468c4f2ddcd84e3d503b24098ec9691465eb3e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TQ3OEU4RJCXKL4TXJ5GFQ3QBSJ/bundle.json","state_url":"https://pith.science/pith/TQ3OEU4RJCXKL4TXJ5GFQ3QBSJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TQ3OEU4RJCXKL4TXJ5GFQ3QBSJ/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":"2026-05-27T21:13:20Z","links":{"resolver":"https://pith.science/pith/TQ3OEU4RJCXKL4TXJ5GFQ3QBSJ","bundle":"https://pith.science/pith/TQ3OEU4RJCXKL4TXJ5GFQ3QBSJ/bundle.json","state":"https://pith.science/pith/TQ3OEU4RJCXKL4TXJ5GFQ3QBSJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TQ3OEU4RJCXKL4TXJ5GFQ3QBSJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TQ3OEU4RJCXKL4TXJ5GFQ3QBSJ","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":"e3d4555bdfc817382252f8f278b9b1d8d2fd657e01b8d3776b925e895b2d1c51","cross_cats_sorted":["cond-mat.soft"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-08-11T02:06:50Z","title_canon_sha256":"800fa36a2c42156ec186888205b929f49bf88f9855c44cfaaceae806d5f4c924"},"schema_version":"1.0","source":{"id":"1608.03347","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03347","created_at":"2026-05-18T01:04:17Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03347v1","created_at":"2026-05-18T01:04:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03347","created_at":"2026-05-18T01:04:17Z"},{"alias_kind":"pith_short_12","alias_value":"TQ3OEU4RJCXK","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TQ3OEU4RJCXKL4TX","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TQ3OEU4R","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:2b27e24eefdf8a96348dabddc3468c4f2ddcd84e3d503b24098ec9691465eb3e","target":"graph","created_at":"2026-05-18T01:04:17Z","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":"Dynamical signatures are known to precede jamming in hard-particle systems, but static structural signatures have proven more elusive. The observation that compressing hard-particle packings towards jamming causes growing hyperuniformity has paved the way for the analysis of jamming as an \"inverted critical point\" in which the direct correlation function $c(r)$ diverges. We establish quantitative relationships between various singularities in $c(r)$ and the total correlation function $h(r)$ that provide a concrete means of identifying features that must be expressed in $c(r)$ if one hopes to r","authors_text":"Frank H. Stillinger, Salvatore Torquato, Steven Atkinson","cross_cats":["cond-mat.soft"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-08-11T02:06:50Z","title":"Static Structural Signatures of Nearly Jammed Disordered and Ordered Hard-Sphere Packings: Direct Correlation Function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03347","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":"sha256:432fd09e60a42fd3419bb6b74437e42f90feda5f82589055ead0565f064d4da1","target":"record","created_at":"2026-05-18T01:04:17Z","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":"e3d4555bdfc817382252f8f278b9b1d8d2fd657e01b8d3776b925e895b2d1c51","cross_cats_sorted":["cond-mat.soft"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-08-11T02:06:50Z","title_canon_sha256":"800fa36a2c42156ec186888205b929f49bf88f9855c44cfaaceae806d5f4c924"},"schema_version":"1.0","source":{"id":"1608.03347","kind":"arxiv","version":1}},"canonical_sha256":"9c36e2539148aea5f2774f4c586e01925550bfacc35d595f0c12743c8df08c2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c36e2539148aea5f2774f4c586e01925550bfacc35d595f0c12743c8df08c2e","first_computed_at":"2026-05-18T01:04:17.805842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:17.805842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0waYv120nyLHueEywVUBXW1jwj1N8Plb0TtzCJp05IdUPQ0Ko0UkfwSzig5vztITuWqGcwm1K2OMTry1ReyaAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:17.806358Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.03347","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:432fd09e60a42fd3419bb6b74437e42f90feda5f82589055ead0565f064d4da1","sha256:2b27e24eefdf8a96348dabddc3468c4f2ddcd84e3d503b24098ec9691465eb3e"],"state_sha256":"99d3c31c9881e0ac2c7e361022265e858f16bf84de64379aa52b7e9c7c95e810"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n9CX18uc8/1RldVCOtm3AMfk3WNy5SfzgCvNQJx5pQFYbBFwX6PYD6TUgnryZKdlZf5VSlGNO6zZ2yNs5uOEDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T21:13:20.026659Z","bundle_sha256":"5033e47e4bde4323a57efe23f85fe0d2e522be328a19eb368a2397696f7eb37e"}}