{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:AAJ57C7R3JJPEELOQSSVBP3QCH","short_pith_number":"pith:AAJ57C7R","canonical_record":{"source":{"id":"2501.05373","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-01-09T16:57:54Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"d1a52c24762eb92b5700442eff061cff371375bd7f524a9e9c5624e0c414c292","abstract_canon_sha256":"de879097c5b6ec841f3d67654d517ad8d7f461263cf86ff0ab1ab6cf64bed1c3"},"schema_version":"1.0"},"canonical_sha256":"0013df8bf1da52f2116e84a550bf7011d3ba5933766117a60666e47b1117c693","source":{"kind":"arxiv","id":"2501.05373","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.05373","created_at":"2026-07-05T09:59:08Z"},{"alias_kind":"arxiv_version","alias_value":"2501.05373v1","created_at":"2026-07-05T09:59:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.05373","created_at":"2026-07-05T09:59:08Z"},{"alias_kind":"pith_short_12","alias_value":"AAJ57C7R3JJP","created_at":"2026-07-05T09:59:08Z"},{"alias_kind":"pith_short_16","alias_value":"AAJ57C7R3JJPEELO","created_at":"2026-07-05T09:59:08Z"},{"alias_kind":"pith_short_8","alias_value":"AAJ57C7R","created_at":"2026-07-05T09:59:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:AAJ57C7R3JJPEELOQSSVBP3QCH","target":"record","payload":{"canonical_record":{"source":{"id":"2501.05373","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-01-09T16:57:54Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"d1a52c24762eb92b5700442eff061cff371375bd7f524a9e9c5624e0c414c292","abstract_canon_sha256":"de879097c5b6ec841f3d67654d517ad8d7f461263cf86ff0ab1ab6cf64bed1c3"},"schema_version":"1.0"},"canonical_sha256":"0013df8bf1da52f2116e84a550bf7011d3ba5933766117a60666e47b1117c693","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:59:08.936414Z","signature_b64":"pDt3stf2SyVCiXcQqgbQ4DkE6vo5LUlomrMCsCdlxYhuU4ow5ZqQYVVTAcvdWpneFIoeHlgjJMc4lmSq1WphDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0013df8bf1da52f2116e84a550bf7011d3ba5933766117a60666e47b1117c693","last_reissued_at":"2026-07-05T09:59:08.936000Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:59:08.936000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.05373","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":"2026-07-05T09:59:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MDJw63YLFR+nphYPBN9BVpWm5e0FKDKVp0Gr4SzOSCX/Yzl6JUvfQCPe8ea7w8q8rR2B5NgkYdcZ5cxYZWqJCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T12:03:38.240146Z"},"content_sha256":"3898b1c495e522a30e85b4f9588c3be47add598131234b957d32616dfac9e8cf","schema_version":"1.0","event_id":"sha256:3898b1c495e522a30e85b4f9588c3be47add598131234b957d32616dfac9e8cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:AAJ57C7R3JJPEELOQSSVBP3QCH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the emergence of almost-honeycomb structures in low-energy planar clusters","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.OC","authors_text":"Francesco Maggi, Kenneth DeMason, Marco Caroccia","submitted_at":"2025-01-09T16:57:54Z","abstract_excerpt":"Several commonly observed physical and biological systems are arranged in shapes that closely resemble an honeycomb cluster, that is, a tessellation of the plane by regular hexagons. Although these shapes are not always the direct product of energy minimization, they can still be understood, at least phenomenologically, as low-energy configurations. In this paper, explicit quantitative estimates on the geometry of such low-energy configurations are provided, showing in particular that the vast majority of the chambers must be generalized polygons with six edges, and be closely resembling regul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.05373","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.05373/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:59:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rgXEyMOd6guhPIJwvKsfeadjcZxxto6HAEf+WxMCoPo7cKsgRrehHptIDAPJYo9iHI/m+n7hdYJAmgsAB/5UBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T12:03:38.241140Z"},"content_sha256":"b6a0d78fe75f918363f22d958f3a44be9cd9a3add740847829d08cd107971790","schema_version":"1.0","event_id":"sha256:b6a0d78fe75f918363f22d958f3a44be9cd9a3add740847829d08cd107971790"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AAJ57C7R3JJPEELOQSSVBP3QCH/bundle.json","state_url":"https://pith.science/pith/AAJ57C7R3JJPEELOQSSVBP3QCH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AAJ57C7R3JJPEELOQSSVBP3QCH/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":"2026-08-10T12:03:38Z","links":{"resolver":"https://pith.science/pith/AAJ57C7R3JJPEELOQSSVBP3QCH","bundle":"https://pith.science/pith/AAJ57C7R3JJPEELOQSSVBP3QCH/bundle.json","state":"https://pith.science/pith/AAJ57C7R3JJPEELOQSSVBP3QCH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AAJ57C7R3JJPEELOQSSVBP3QCH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:AAJ57C7R3JJPEELOQSSVBP3QCH","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":"de879097c5b6ec841f3d67654d517ad8d7f461263cf86ff0ab1ab6cf64bed1c3","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-01-09T16:57:54Z","title_canon_sha256":"d1a52c24762eb92b5700442eff061cff371375bd7f524a9e9c5624e0c414c292"},"schema_version":"1.0","source":{"id":"2501.05373","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.05373","created_at":"2026-07-05T09:59:08Z"},{"alias_kind":"arxiv_version","alias_value":"2501.05373v1","created_at":"2026-07-05T09:59:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.05373","created_at":"2026-07-05T09:59:08Z"},{"alias_kind":"pith_short_12","alias_value":"AAJ57C7R3JJP","created_at":"2026-07-05T09:59:08Z"},{"alias_kind":"pith_short_16","alias_value":"AAJ57C7R3JJPEELO","created_at":"2026-07-05T09:59:08Z"},{"alias_kind":"pith_short_8","alias_value":"AAJ57C7R","created_at":"2026-07-05T09:59:08Z"}],"graph_snapshots":[{"event_id":"sha256:b6a0d78fe75f918363f22d958f3a44be9cd9a3add740847829d08cd107971790","target":"graph","created_at":"2026-07-05T09:59:08Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.05373/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Several commonly observed physical and biological systems are arranged in shapes that closely resemble an honeycomb cluster, that is, a tessellation of the plane by regular hexagons. Although these shapes are not always the direct product of energy minimization, they can still be understood, at least phenomenologically, as low-energy configurations. In this paper, explicit quantitative estimates on the geometry of such low-energy configurations are provided, showing in particular that the vast majority of the chambers must be generalized polygons with six edges, and be closely resembling regul","authors_text":"Francesco Maggi, Kenneth DeMason, Marco Caroccia","cross_cats":["math-ph","math.DG","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-01-09T16:57:54Z","title":"On the emergence of almost-honeycomb structures in low-energy planar clusters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.05373","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":"sha256:3898b1c495e522a30e85b4f9588c3be47add598131234b957d32616dfac9e8cf","target":"record","created_at":"2026-07-05T09:59:08Z","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":"de879097c5b6ec841f3d67654d517ad8d7f461263cf86ff0ab1ab6cf64bed1c3","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-01-09T16:57:54Z","title_canon_sha256":"d1a52c24762eb92b5700442eff061cff371375bd7f524a9e9c5624e0c414c292"},"schema_version":"1.0","source":{"id":"2501.05373","kind":"arxiv","version":1}},"canonical_sha256":"0013df8bf1da52f2116e84a550bf7011d3ba5933766117a60666e47b1117c693","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0013df8bf1da52f2116e84a550bf7011d3ba5933766117a60666e47b1117c693","first_computed_at":"2026-07-05T09:59:08.936000Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:59:08.936000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pDt3stf2SyVCiXcQqgbQ4DkE6vo5LUlomrMCsCdlxYhuU4ow5ZqQYVVTAcvdWpneFIoeHlgjJMc4lmSq1WphDg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:59:08.936414Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.05373","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3898b1c495e522a30e85b4f9588c3be47add598131234b957d32616dfac9e8cf","sha256:b6a0d78fe75f918363f22d958f3a44be9cd9a3add740847829d08cd107971790"],"state_sha256":"627d964600e0e69c3efde102ee304743c3df6c220664e5721c94423f9cad3151"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TW0OT1BAZkY/RK+w2mJDg3QUXcHPUooAv3DlVQop4lsICuGFnnIXvUOFMSfonHHMdHCxfHFPClJjQss/RjqGCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T12:03:38.246615Z","bundle_sha256":"408eb452d28f8d5213ad8fda2cdfe5dcd6f12ff0c4b99c57b32eff0b37851b75"}}