{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:YKKY3XII2ID72RK6SZ44XKYNZS","short_pith_number":"pith:YKKY3XII","canonical_record":{"source":{"id":"1111.4917","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-11-21T16:22:23Z","cross_cats_sorted":["cond-mat.mtrl-sci","cond-mat.soft"],"title_canon_sha256":"1036b1237fbde101e63cd534c4fe47c70acd4eff69444e919ba345cd241a6e60","abstract_canon_sha256":"0d731476a908c1f16e6345ba391cb64f0d6830259961d43bd8437a532cfedcd9"},"schema_version":"1.0"},"canonical_sha256":"c2958ddd08d207fd455e9679cbab0dcc87effeaa1162bd2af2cae7e9caeb2c5b","source":{"kind":"arxiv","id":"1111.4917","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4917","created_at":"2026-05-18T01:59:27Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4917v2","created_at":"2026-05-18T01:59:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4917","created_at":"2026-05-18T01:59:27Z"},{"alias_kind":"pith_short_12","alias_value":"YKKY3XII2ID7","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YKKY3XII2ID72RK6","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YKKY3XII","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:YKKY3XII2ID72RK6SZ44XKYNZS","target":"record","payload":{"canonical_record":{"source":{"id":"1111.4917","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-11-21T16:22:23Z","cross_cats_sorted":["cond-mat.mtrl-sci","cond-mat.soft"],"title_canon_sha256":"1036b1237fbde101e63cd534c4fe47c70acd4eff69444e919ba345cd241a6e60","abstract_canon_sha256":"0d731476a908c1f16e6345ba391cb64f0d6830259961d43bd8437a532cfedcd9"},"schema_version":"1.0"},"canonical_sha256":"c2958ddd08d207fd455e9679cbab0dcc87effeaa1162bd2af2cae7e9caeb2c5b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:27.429467Z","signature_b64":"UY64nP70yzpCgf1szwqNfmsLvwVu39DNlokMS45siyJEQ/L0pgIWnqDE6vVRN29/EdmM9vY0cIJiZpnpu831Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2958ddd08d207fd455e9679cbab0dcc87effeaa1162bd2af2cae7e9caeb2c5b","last_reissued_at":"2026-05-18T01:59:27.428879Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:27.428879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.4917","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":"2026-05-18T01:59:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s4xx31phyinGl0pf0RFtMNUzE4kiTygU74R/gWUabmsZzSrOAVFd9kEGIb1XLL6XhBlsPHDoJMpogZt4CWAFDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:59:24.376999Z"},"content_sha256":"c4ef3ae12370a7e77053a68a4149f3e53f3c6f05b42344552e53416a53fb2343","schema_version":"1.0","event_id":"sha256:c4ef3ae12370a7e77053a68a4149f3e53f3c6f05b42344552e53416a53fb2343"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:YKKY3XII2ID72RK6SZ44XKYNZS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Densest binary sphere packings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","cond-mat.soft"],"primary_cat":"cond-mat.stat-mech","authors_text":"Adam B. Hopkins, Frank H. Stillinger, Salvatore Torquato","submitted_at":"2011-11-21T16:22:23Z","abstract_excerpt":"The densest binary sphere packings in the alpha-x plane of small to large sphere radius ratio alpha and small sphere relative concentration x have historically been very difficult to determine. Previous research had led to the prediction that these packings were composed of a few known \"alloy\" phases including, for example, the AlB2 (hexagonal omega), HgBr2, and AuTe2 structures, and to XYn structures composed of close-packed large spheres with small spheres (in a number ratio of n to 1) in the interstices, e.g., the NaCl packing for n = 1. However, utilizing an implementation of the Torquato-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4917","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":"2026-05-18T01:59:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BJaI7kmosB2f/1N6XUIwz8eczkMudRqGSYYLgjIyWhkhCQIQg/qQ/0UDFGhn1tpt7PLiXlaWP3xPC1B2l4ogBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:59:24.377435Z"},"content_sha256":"e85cdae74f8edcab240cf926718fc1503df6d2ee9d28115612734c7cf25de5f6","schema_version":"1.0","event_id":"sha256:e85cdae74f8edcab240cf926718fc1503df6d2ee9d28115612734c7cf25de5f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YKKY3XII2ID72RK6SZ44XKYNZS/bundle.json","state_url":"https://pith.science/pith/YKKY3XII2ID72RK6SZ44XKYNZS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YKKY3XII2ID72RK6SZ44XKYNZS/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":"2026-05-26T21:59:24Z","links":{"resolver":"https://pith.science/pith/YKKY3XII2ID72RK6SZ44XKYNZS","bundle":"https://pith.science/pith/YKKY3XII2ID72RK6SZ44XKYNZS/bundle.json","state":"https://pith.science/pith/YKKY3XII2ID72RK6SZ44XKYNZS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YKKY3XII2ID72RK6SZ44XKYNZS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YKKY3XII2ID72RK6SZ44XKYNZS","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":"0d731476a908c1f16e6345ba391cb64f0d6830259961d43bd8437a532cfedcd9","cross_cats_sorted":["cond-mat.mtrl-sci","cond-mat.soft"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-11-21T16:22:23Z","title_canon_sha256":"1036b1237fbde101e63cd534c4fe47c70acd4eff69444e919ba345cd241a6e60"},"schema_version":"1.0","source":{"id":"1111.4917","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4917","created_at":"2026-05-18T01:59:27Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4917v2","created_at":"2026-05-18T01:59:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4917","created_at":"2026-05-18T01:59:27Z"},{"alias_kind":"pith_short_12","alias_value":"YKKY3XII2ID7","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YKKY3XII2ID72RK6","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YKKY3XII","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:e85cdae74f8edcab240cf926718fc1503df6d2ee9d28115612734c7cf25de5f6","target":"graph","created_at":"2026-05-18T01:59:27Z","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 binary sphere packings in the alpha-x plane of small to large sphere radius ratio alpha and small sphere relative concentration x have historically been very difficult to determine. Previous research had led to the prediction that these packings were composed of a few known \"alloy\" phases including, for example, the AlB2 (hexagonal omega), HgBr2, and AuTe2 structures, and to XYn structures composed of close-packed large spheres with small spheres (in a number ratio of n to 1) in the interstices, e.g., the NaCl packing for n = 1. However, utilizing an implementation of the Torquato-","authors_text":"Adam B. Hopkins, Frank H. Stillinger, Salvatore Torquato","cross_cats":["cond-mat.mtrl-sci","cond-mat.soft"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-11-21T16:22:23Z","title":"Densest binary sphere packings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4917","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:c4ef3ae12370a7e77053a68a4149f3e53f3c6f05b42344552e53416a53fb2343","target":"record","created_at":"2026-05-18T01:59:27Z","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":"0d731476a908c1f16e6345ba391cb64f0d6830259961d43bd8437a532cfedcd9","cross_cats_sorted":["cond-mat.mtrl-sci","cond-mat.soft"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-11-21T16:22:23Z","title_canon_sha256":"1036b1237fbde101e63cd534c4fe47c70acd4eff69444e919ba345cd241a6e60"},"schema_version":"1.0","source":{"id":"1111.4917","kind":"arxiv","version":2}},"canonical_sha256":"c2958ddd08d207fd455e9679cbab0dcc87effeaa1162bd2af2cae7e9caeb2c5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2958ddd08d207fd455e9679cbab0dcc87effeaa1162bd2af2cae7e9caeb2c5b","first_computed_at":"2026-05-18T01:59:27.428879Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:27.428879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UY64nP70yzpCgf1szwqNfmsLvwVu39DNlokMS45siyJEQ/L0pgIWnqDE6vVRN29/EdmM9vY0cIJiZpnpu831Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:27.429467Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.4917","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4ef3ae12370a7e77053a68a4149f3e53f3c6f05b42344552e53416a53fb2343","sha256:e85cdae74f8edcab240cf926718fc1503df6d2ee9d28115612734c7cf25de5f6"],"state_sha256":"7967e6301bd54b32b75fb8aeebd44a45fe301a7efe57240147f9159b065388be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XPHxaQCNf1eLcI9YcJduIrZLCGQ7CzteGW1DBRm3l1AgmiF1J+EOJ0Y5r5RbUbzKZLPQfeGKA7kR0eP1gWdnAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:59:24.379595Z","bundle_sha256":"93c462f717da24e7e3d56afff75205c996dc2237cd132db22260a64894ada1c0"}}