{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:T5QE6U3TM6HGMSQ6HKOVAU3N62","short_pith_number":"pith:T5QE6U3T","canonical_record":{"source":{"id":"1402.6745","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-02-26T23:30:43Z","cross_cats_sorted":["cond-mat.soft"],"title_canon_sha256":"cd45acc9d710131de0c79dcebcc10342dc930499861b24c882679111882b88c8","abstract_canon_sha256":"27cc438133b48bf9fd71e1a1f649f2a0a701049277af71523a3ff8c89b711c5c"},"schema_version":"1.0"},"canonical_sha256":"9f604f5373678e664a1e3a9d50536df6aa046f891a564380db5d2ec0c22d2700","source":{"kind":"arxiv","id":"1402.6745","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6745","created_at":"2026-05-18T02:57:43Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6745v1","created_at":"2026-05-18T02:57:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6745","created_at":"2026-05-18T02:57:43Z"},{"alias_kind":"pith_short_12","alias_value":"T5QE6U3TM6HG","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"T5QE6U3TM6HGMSQ6","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"T5QE6U3T","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:T5QE6U3TM6HGMSQ6HKOVAU3N62","target":"record","payload":{"canonical_record":{"source":{"id":"1402.6745","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-02-26T23:30:43Z","cross_cats_sorted":["cond-mat.soft"],"title_canon_sha256":"cd45acc9d710131de0c79dcebcc10342dc930499861b24c882679111882b88c8","abstract_canon_sha256":"27cc438133b48bf9fd71e1a1f649f2a0a701049277af71523a3ff8c89b711c5c"},"schema_version":"1.0"},"canonical_sha256":"9f604f5373678e664a1e3a9d50536df6aa046f891a564380db5d2ec0c22d2700","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:43.009187Z","signature_b64":"382d4qLsskmlIgaaftGlSQJdJMSrj+EhcqEhJrKDHLdYQFoRFcz1S09TBscDPwGOkjfbKFRXXs7GNsNRzfPSAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f604f5373678e664a1e3a9d50536df6aa046f891a564380db5d2ec0c22d2700","last_reissued_at":"2026-05-18T02:57:43.008714Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:43.008714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.6745","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":"2026-05-18T02:57:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t9GAC5YiDF+Ul/LvTSiibfOHIK+Y2MeGrBkJ4iXm37zZHDLfZHh5IRg6as0ODCdtrKLuDJNxfFuPHwhP0ZvJBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:24:08.898641Z"},"content_sha256":"df38868642625c92c7e317397523ffaeddddf9d15015ba327b39d29ca29a2720","schema_version":"1.0","event_id":"sha256:df38868642625c92c7e317397523ffaeddddf9d15015ba327b39d29ca29a2720"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:T5QE6U3TM6HGMSQ6HKOVAU3N62","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dense periodic packings of tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft"],"primary_cat":"cond-mat.stat-mech","authors_text":"Ruggero Gabbrielli, Salvatore Torquato, Yang Jiao","submitted_at":"2014-02-26T23:30:43Z","abstract_excerpt":"Dense packings of nonoverlapping bodies in three-dimensional Euclidean space are useful models of the structure of a variety of many-particle systems that arise in the physical and biological sciences. Here we investigate the packing behavior of congruent ring tori, which are multiply connected nonconvex bodies of genus 1, as well as horn and spindle tori. We analytically construct a family of dense periodic packings of unlinked tori guided by the organizing principles originally devised for simply connected solid bodies [Torquato and Jiao, PRE 86, 011102 (2012)]. We find that the horn tori as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6745","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":"2026-05-18T02:57:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TpzNzuMjQO7/QCWcK6O0npVPvy084C/hPGcsEFjzQ/v04Th4pb+EJCYGSbVsjcpti2m7wgvYSwJqjKFB8MxdDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:24:08.898988Z"},"content_sha256":"5b81a044d07d502e6d88fe35ffb2a32e430ee9895a87a205fc0d2d756af8c537","schema_version":"1.0","event_id":"sha256:5b81a044d07d502e6d88fe35ffb2a32e430ee9895a87a205fc0d2d756af8c537"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T5QE6U3TM6HGMSQ6HKOVAU3N62/bundle.json","state_url":"https://pith.science/pith/T5QE6U3TM6HGMSQ6HKOVAU3N62/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T5QE6U3TM6HGMSQ6HKOVAU3N62/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":"2026-06-23T06:24:08Z","links":{"resolver":"https://pith.science/pith/T5QE6U3TM6HGMSQ6HKOVAU3N62","bundle":"https://pith.science/pith/T5QE6U3TM6HGMSQ6HKOVAU3N62/bundle.json","state":"https://pith.science/pith/T5QE6U3TM6HGMSQ6HKOVAU3N62/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T5QE6U3TM6HGMSQ6HKOVAU3N62/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:T5QE6U3TM6HGMSQ6HKOVAU3N62","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":"27cc438133b48bf9fd71e1a1f649f2a0a701049277af71523a3ff8c89b711c5c","cross_cats_sorted":["cond-mat.soft"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-02-26T23:30:43Z","title_canon_sha256":"cd45acc9d710131de0c79dcebcc10342dc930499861b24c882679111882b88c8"},"schema_version":"1.0","source":{"id":"1402.6745","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6745","created_at":"2026-05-18T02:57:43Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6745v1","created_at":"2026-05-18T02:57:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6745","created_at":"2026-05-18T02:57:43Z"},{"alias_kind":"pith_short_12","alias_value":"T5QE6U3TM6HG","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"T5QE6U3TM6HGMSQ6","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"T5QE6U3T","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:5b81a044d07d502e6d88fe35ffb2a32e430ee9895a87a205fc0d2d756af8c537","target":"graph","created_at":"2026-05-18T02:57:43Z","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":"Dense packings of nonoverlapping bodies in three-dimensional Euclidean space are useful models of the structure of a variety of many-particle systems that arise in the physical and biological sciences. Here we investigate the packing behavior of congruent ring tori, which are multiply connected nonconvex bodies of genus 1, as well as horn and spindle tori. We analytically construct a family of dense periodic packings of unlinked tori guided by the organizing principles originally devised for simply connected solid bodies [Torquato and Jiao, PRE 86, 011102 (2012)]. We find that the horn tori as","authors_text":"Ruggero Gabbrielli, Salvatore Torquato, Yang Jiao","cross_cats":["cond-mat.soft"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-02-26T23:30:43Z","title":"Dense periodic packings of tori"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6745","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:df38868642625c92c7e317397523ffaeddddf9d15015ba327b39d29ca29a2720","target":"record","created_at":"2026-05-18T02:57:43Z","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":"27cc438133b48bf9fd71e1a1f649f2a0a701049277af71523a3ff8c89b711c5c","cross_cats_sorted":["cond-mat.soft"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-02-26T23:30:43Z","title_canon_sha256":"cd45acc9d710131de0c79dcebcc10342dc930499861b24c882679111882b88c8"},"schema_version":"1.0","source":{"id":"1402.6745","kind":"arxiv","version":1}},"canonical_sha256":"9f604f5373678e664a1e3a9d50536df6aa046f891a564380db5d2ec0c22d2700","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f604f5373678e664a1e3a9d50536df6aa046f891a564380db5d2ec0c22d2700","first_computed_at":"2026-05-18T02:57:43.008714Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:43.008714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"382d4qLsskmlIgaaftGlSQJdJMSrj+EhcqEhJrKDHLdYQFoRFcz1S09TBscDPwGOkjfbKFRXXs7GNsNRzfPSAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:43.009187Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.6745","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df38868642625c92c7e317397523ffaeddddf9d15015ba327b39d29ca29a2720","sha256:5b81a044d07d502e6d88fe35ffb2a32e430ee9895a87a205fc0d2d756af8c537"],"state_sha256":"ad5cd684f3e0f6796d100421e256e95bc5aa4a193f5223b4c0060da116393808"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bFZiO9RRGZm2CyPZn1kkIO5nsKGiz3pdHKiSUy86h0IG3jxtwsQUj8PU0HZvRhBY1lLhWdBYHQ5ViUbrzCRCBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T06:24:08.900877Z","bundle_sha256":"57abd92c418ce2d3bb6f252d9c746f791103c53905b480042fc61f8ff1c7d4dc"}}