{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:CJSPKXHF22G4FS3CG42TTS2BN5","short_pith_number":"pith:CJSPKXHF","canonical_record":{"source":{"id":"1003.3604","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-03-18T15:13:02Z","cross_cats_sorted":["cond-mat.soft","math.MG"],"title_canon_sha256":"fc1ed76053e81fe8624ca2b906508fb5f0d5956163e00e857275ca643ae87570","abstract_canon_sha256":"d21efa661820e2c08083b97502211b3a57d47a4625784477de9b4dd04082dfe7"},"schema_version":"1.0"},"canonical_sha256":"1264f55ce5d68dc2cb62373539cb416f72dbb25aa65d0c62c38547d951a11fcc","source":{"kind":"arxiv","id":"1003.3604","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.3604","created_at":"2026-05-18T02:08:25Z"},{"alias_kind":"arxiv_version","alias_value":"1003.3604v1","created_at":"2026-05-18T02:08:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.3604","created_at":"2026-05-18T02:08:25Z"},{"alias_kind":"pith_short_12","alias_value":"CJSPKXHF22G4","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"CJSPKXHF22G4FS3C","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"CJSPKXHF","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:CJSPKXHF22G4FS3CG42TTS2BN5","target":"record","payload":{"canonical_record":{"source":{"id":"1003.3604","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-03-18T15:13:02Z","cross_cats_sorted":["cond-mat.soft","math.MG"],"title_canon_sha256":"fc1ed76053e81fe8624ca2b906508fb5f0d5956163e00e857275ca643ae87570","abstract_canon_sha256":"d21efa661820e2c08083b97502211b3a57d47a4625784477de9b4dd04082dfe7"},"schema_version":"1.0"},"canonical_sha256":"1264f55ce5d68dc2cb62373539cb416f72dbb25aa65d0c62c38547d951a11fcc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:08:25.959727Z","signature_b64":"cpsSz7wGKMG2TZe/sbxuHuvR7ypXXaqT+ZUzsRiQJlNyxWQr1gTBtkihbTzOmvpiWyN1mGoM9G4vLMKJexbqCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1264f55ce5d68dc2cb62373539cb416f72dbb25aa65d0c62c38547d951a11fcc","last_reissued_at":"2026-05-18T02:08:25.959199Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:08:25.959199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.3604","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":"2026-05-18T02:08:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jnfrhdK2cAxShuNqI+LP4Hr5H8ciutNsy8kq552dbhb3E33HZ2Eu3cFNzWrKqm8X85hFCpUDGZWBuqkcbUz9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:00:18.671665Z"},"content_sha256":"3baa03ba7e350a21fc3ef6e26472c6e355886039b97baf3dae4072d4c2c72a3b","schema_version":"1.0","event_id":"sha256:3baa03ba7e350a21fc3ef6e26472c6e355886039b97baf3dae4072d4c2c72a3b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:CJSPKXHF22G4FS3CG42TTS2BN5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spherical codes, maximal local packing density, and the golden ratio","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft","math.MG"],"primary_cat":"cond-mat.stat-mech","authors_text":"A. B. Hopkins, F. H. Stillinger, S. Torquato","submitted_at":"2010-03-18T15:13:02Z","abstract_excerpt":"The densest local packing (DLP) problem in d-dimensional Euclidean space Rd involves the placement of N nonoverlapping spheres of unit diameter near an additional fixed unit-diameter sphere such that the greatest distance from the center of the fixed sphere to the centers of any of the N surrounding spheres is minimized. Solutions to the DLP problem are relevant to the realizability of pair correlation functions for packings of nonoverlapping spheres and might prove useful in improving upon the best known upper bounds on the maximum packing fraction of sphere packings in dimensions greater tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.3604","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":"2026-05-18T02:08:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O6+PWhSO4CO165zzk+MXsjzFbGkOkvhnGKjNfEYs6gVi537rYPkBnKHo0k/XpET/sWNcqgf0NqcCPow2ezN4Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:00:18.672007Z"},"content_sha256":"d912647e62db2b35e3144b18e5943fa327fed3f4c59b1e2d905be0f7d3a0e9d1","schema_version":"1.0","event_id":"sha256:d912647e62db2b35e3144b18e5943fa327fed3f4c59b1e2d905be0f7d3a0e9d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CJSPKXHF22G4FS3CG42TTS2BN5/bundle.json","state_url":"https://pith.science/pith/CJSPKXHF22G4FS3CG42TTS2BN5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CJSPKXHF22G4FS3CG42TTS2BN5/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":"2026-06-01T20:00:18Z","links":{"resolver":"https://pith.science/pith/CJSPKXHF22G4FS3CG42TTS2BN5","bundle":"https://pith.science/pith/CJSPKXHF22G4FS3CG42TTS2BN5/bundle.json","state":"https://pith.science/pith/CJSPKXHF22G4FS3CG42TTS2BN5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CJSPKXHF22G4FS3CG42TTS2BN5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:CJSPKXHF22G4FS3CG42TTS2BN5","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":"d21efa661820e2c08083b97502211b3a57d47a4625784477de9b4dd04082dfe7","cross_cats_sorted":["cond-mat.soft","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-03-18T15:13:02Z","title_canon_sha256":"fc1ed76053e81fe8624ca2b906508fb5f0d5956163e00e857275ca643ae87570"},"schema_version":"1.0","source":{"id":"1003.3604","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.3604","created_at":"2026-05-18T02:08:25Z"},{"alias_kind":"arxiv_version","alias_value":"1003.3604v1","created_at":"2026-05-18T02:08:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.3604","created_at":"2026-05-18T02:08:25Z"},{"alias_kind":"pith_short_12","alias_value":"CJSPKXHF22G4","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"CJSPKXHF22G4FS3C","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"CJSPKXHF","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:d912647e62db2b35e3144b18e5943fa327fed3f4c59b1e2d905be0f7d3a0e9d1","target":"graph","created_at":"2026-05-18T02:08:25Z","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":"The densest local packing (DLP) problem in d-dimensional Euclidean space Rd involves the placement of N nonoverlapping spheres of unit diameter near an additional fixed unit-diameter sphere such that the greatest distance from the center of the fixed sphere to the centers of any of the N surrounding spheres is minimized. Solutions to the DLP problem are relevant to the realizability of pair correlation functions for packings of nonoverlapping spheres and might prove useful in improving upon the best known upper bounds on the maximum packing fraction of sphere packings in dimensions greater tha","authors_text":"A. B. Hopkins, F. H. Stillinger, S. Torquato","cross_cats":["cond-mat.soft","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-03-18T15:13:02Z","title":"Spherical codes, maximal local packing density, and the golden ratio"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.3604","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":"sha256:3baa03ba7e350a21fc3ef6e26472c6e355886039b97baf3dae4072d4c2c72a3b","target":"record","created_at":"2026-05-18T02:08:25Z","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":"d21efa661820e2c08083b97502211b3a57d47a4625784477de9b4dd04082dfe7","cross_cats_sorted":["cond-mat.soft","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-03-18T15:13:02Z","title_canon_sha256":"fc1ed76053e81fe8624ca2b906508fb5f0d5956163e00e857275ca643ae87570"},"schema_version":"1.0","source":{"id":"1003.3604","kind":"arxiv","version":1}},"canonical_sha256":"1264f55ce5d68dc2cb62373539cb416f72dbb25aa65d0c62c38547d951a11fcc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1264f55ce5d68dc2cb62373539cb416f72dbb25aa65d0c62c38547d951a11fcc","first_computed_at":"2026-05-18T02:08:25.959199Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:08:25.959199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cpsSz7wGKMG2TZe/sbxuHuvR7ypXXaqT+ZUzsRiQJlNyxWQr1gTBtkihbTzOmvpiWyN1mGoM9G4vLMKJexbqCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:08:25.959727Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.3604","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3baa03ba7e350a21fc3ef6e26472c6e355886039b97baf3dae4072d4c2c72a3b","sha256:d912647e62db2b35e3144b18e5943fa327fed3f4c59b1e2d905be0f7d3a0e9d1"],"state_sha256":"b933298549948b015917fb7720d1b1fbdfb0c78d32aa7d3ad8b91bd628837fd2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qeNvn9Br9DuOSPkxwryT3SJ44FdyfJeocEmQCQSYKJ7YiqfyWVA581kcAN7EcKCU6f//aTyO6Fq+x92TTDUNDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T20:00:18.673935Z","bundle_sha256":"c30461114fd9bdd3a1d8d354c77ffaca27233a55502ebf335314e669609db8be"}}