{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:IR6SSIPRUJI5FJKYWPLMNPG6BQ","short_pith_number":"pith:IR6SSIPR","canonical_record":{"source":{"id":"2506.22614","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2025-06-27T20:21:30Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d630c99efe96f5ace72d02f6701ed2dedce2181e3a66248f4e4c9836dea665dd","abstract_canon_sha256":"6240cf2067e2b83e23d64e59c7aaafaf0e3c473a5a57fe329669c85ba755fa09"},"schema_version":"1.0"},"canonical_sha256":"447d2921f1a251d2a558b3d6c6bcde0c2bf5b66c05d80201376c20c22d348654","source":{"kind":"arxiv","id":"2506.22614","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.22614","created_at":"2026-06-09T01:05:07Z"},{"alias_kind":"arxiv_version","alias_value":"2506.22614v3","created_at":"2026-06-09T01:05:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.22614","created_at":"2026-06-09T01:05:07Z"},{"alias_kind":"pith_short_12","alias_value":"IR6SSIPRUJI5","created_at":"2026-06-09T01:05:07Z"},{"alias_kind":"pith_short_16","alias_value":"IR6SSIPRUJI5FJKY","created_at":"2026-06-09T01:05:07Z"},{"alias_kind":"pith_short_8","alias_value":"IR6SSIPR","created_at":"2026-06-09T01:05:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:IR6SSIPRUJI5FJKYWPLMNPG6BQ","target":"record","payload":{"canonical_record":{"source":{"id":"2506.22614","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2025-06-27T20:21:30Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d630c99efe96f5ace72d02f6701ed2dedce2181e3a66248f4e4c9836dea665dd","abstract_canon_sha256":"6240cf2067e2b83e23d64e59c7aaafaf0e3c473a5a57fe329669c85ba755fa09"},"schema_version":"1.0"},"canonical_sha256":"447d2921f1a251d2a558b3d6c6bcde0c2bf5b66c05d80201376c20c22d348654","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:05:07.499206Z","signature_b64":"Ew7eT+xCr1lUEvEAxR3joZzNOIBHHhgmM/LUHn7GHVt4O/XSVcGxTb/g3OCmpyI18pBIALJdryJmXwM5nVKTDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"447d2921f1a251d2a558b3d6c6bcde0c2bf5b66c05d80201376c20c22d348654","last_reissued_at":"2026-06-09T01:05:07.498426Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:05:07.498426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.22614","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-09T01:05:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uuj53rRn86O+0SPXNa4dXRj7lmoBGhZwTYxDsvmoSw+gRM9xsvs5HtSkwrnrWlKR32oTdDsiKk48KQI69e5pBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:57:18.259425Z"},"content_sha256":"d044115b3d7dd298e4f1c089417fdeb0515a3dd2e842ea348a22d0ec3829b32c","schema_version":"1.0","event_id":"sha256:d044115b3d7dd298e4f1c089417fdeb0515a3dd2e842ea348a22d0ec3829b32c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:IR6SSIPRUJI5FJKYWPLMNPG6BQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computer-Assisted Proofs for Geometric Optimization: From Crystallization to Carbon Nanotubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"physics.comp-ph","authors_text":"Benedikt Wirth, Miguel Ayala, Rustum Choksi","submitted_at":"2025-06-27T20:21:30Z","abstract_excerpt":"We present a framework based on computer-assisted proofs that turns geometry optimization simulations for atomistic structures into mathematical proofs. Starting from a numerically computed approximation of a local minimizer or saddle point, we use validated numerical computations to prove the existence of a critical point of the potential energy close to this approximation. We demonstrate this framework in two settings. In the first, we study capped carbon nanotubes modeled as minimizers of carbon interatomic potentials (harmonic, Tersoff, and a Huber potential) and obtain proven bounds on tu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.22614","kind":"arxiv","version":3},"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/2506.22614/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":"2026-06-09T01:05:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CCeaLCBX8Sh58TMZFrig0w/2ZotmHtdGtbV82O6FGV20Bz2faIekeJfSURhC+G0rkWKlWWAXApW2+2NP6qt5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:57:18.259887Z"},"content_sha256":"48a704860a1fa586ac4aa973f46c5a98727619737486c8b1446ec66968ed24f5","schema_version":"1.0","event_id":"sha256:48a704860a1fa586ac4aa973f46c5a98727619737486c8b1446ec66968ed24f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IR6SSIPRUJI5FJKYWPLMNPG6BQ/bundle.json","state_url":"https://pith.science/pith/IR6SSIPRUJI5FJKYWPLMNPG6BQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IR6SSIPRUJI5FJKYWPLMNPG6BQ/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":"2026-06-10T22:57:18Z","links":{"resolver":"https://pith.science/pith/IR6SSIPRUJI5FJKYWPLMNPG6BQ","bundle":"https://pith.science/pith/IR6SSIPRUJI5FJKYWPLMNPG6BQ/bundle.json","state":"https://pith.science/pith/IR6SSIPRUJI5FJKYWPLMNPG6BQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IR6SSIPRUJI5FJKYWPLMNPG6BQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:IR6SSIPRUJI5FJKYWPLMNPG6BQ","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":"6240cf2067e2b83e23d64e59c7aaafaf0e3c473a5a57fe329669c85ba755fa09","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2025-06-27T20:21:30Z","title_canon_sha256":"d630c99efe96f5ace72d02f6701ed2dedce2181e3a66248f4e4c9836dea665dd"},"schema_version":"1.0","source":{"id":"2506.22614","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.22614","created_at":"2026-06-09T01:05:07Z"},{"alias_kind":"arxiv_version","alias_value":"2506.22614v3","created_at":"2026-06-09T01:05:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.22614","created_at":"2026-06-09T01:05:07Z"},{"alias_kind":"pith_short_12","alias_value":"IR6SSIPRUJI5","created_at":"2026-06-09T01:05:07Z"},{"alias_kind":"pith_short_16","alias_value":"IR6SSIPRUJI5FJKY","created_at":"2026-06-09T01:05:07Z"},{"alias_kind":"pith_short_8","alias_value":"IR6SSIPR","created_at":"2026-06-09T01:05:07Z"}],"graph_snapshots":[{"event_id":"sha256:48a704860a1fa586ac4aa973f46c5a98727619737486c8b1446ec66968ed24f5","target":"graph","created_at":"2026-06-09T01:05:07Z","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/2506.22614/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a framework based on computer-assisted proofs that turns geometry optimization simulations for atomistic structures into mathematical proofs. Starting from a numerically computed approximation of a local minimizer or saddle point, we use validated numerical computations to prove the existence of a critical point of the potential energy close to this approximation. We demonstrate this framework in two settings. In the first, we study capped carbon nanotubes modeled as minimizers of carbon interatomic potentials (harmonic, Tersoff, and a Huber potential) and obtain proven bounds on tu","authors_text":"Benedikt Wirth, Miguel Ayala, Rustum Choksi","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2025-06-27T20:21:30Z","title":"Computer-Assisted Proofs for Geometric Optimization: From Crystallization to Carbon Nanotubes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.22614","kind":"arxiv","version":3},"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:d044115b3d7dd298e4f1c089417fdeb0515a3dd2e842ea348a22d0ec3829b32c","target":"record","created_at":"2026-06-09T01:05:07Z","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":"6240cf2067e2b83e23d64e59c7aaafaf0e3c473a5a57fe329669c85ba755fa09","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2025-06-27T20:21:30Z","title_canon_sha256":"d630c99efe96f5ace72d02f6701ed2dedce2181e3a66248f4e4c9836dea665dd"},"schema_version":"1.0","source":{"id":"2506.22614","kind":"arxiv","version":3}},"canonical_sha256":"447d2921f1a251d2a558b3d6c6bcde0c2bf5b66c05d80201376c20c22d348654","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"447d2921f1a251d2a558b3d6c6bcde0c2bf5b66c05d80201376c20c22d348654","first_computed_at":"2026-06-09T01:05:07.498426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:05:07.498426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ew7eT+xCr1lUEvEAxR3joZzNOIBHHhgmM/LUHn7GHVt4O/XSVcGxTb/g3OCmpyI18pBIALJdryJmXwM5nVKTDw==","signature_status":"signed_v1","signed_at":"2026-06-09T01:05:07.499206Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.22614","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d044115b3d7dd298e4f1c089417fdeb0515a3dd2e842ea348a22d0ec3829b32c","sha256:48a704860a1fa586ac4aa973f46c5a98727619737486c8b1446ec66968ed24f5"],"state_sha256":"b9c663a129bec90486dd4a24b47f667414aa79bdeb53b6a92347c20c973ff238"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WNXyNJLswrhwID85RwYh+TOmcACn+fZKyLyCtYqGHnwOHRijbwWL2YwfQOOBmO1hsxvAuj+Kcx0gzJmiLjpWCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T22:57:18.262889Z","bundle_sha256":"a645b3ff17c19a43226c6e7c354cad9588cdda30a4fcf5cd9ce7bac14c75a457"}}