{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:DGG67WW4EMK7544XKHZFTT6LM2","short_pith_number":"pith:DGG67WW4","canonical_record":{"source":{"id":"1809.06110","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-09-17T10:18:25Z","cross_cats_sorted":["math.AP","math.MP","math.SP"],"title_canon_sha256":"ee407dfb39f8618bc32cfa127241459f092e6534a7374907e578a44376701782","abstract_canon_sha256":"8c6b13cb36d1c4e52f295efac5e80d153ff4d7ac383e56ea26f6f98dd7bca51e"},"schema_version":"1.0"},"canonical_sha256":"198defdadc2315fef39751f259cfcb66adf67435e08ce4f6f8597acc53956a3d","source":{"kind":"arxiv","id":"1809.06110","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.06110","created_at":"2026-07-05T00:23:20Z"},{"alias_kind":"arxiv_version","alias_value":"1809.06110v2","created_at":"2026-07-05T00:23:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.06110","created_at":"2026-07-05T00:23:20Z"},{"alias_kind":"pith_short_12","alias_value":"DGG67WW4EMK7","created_at":"2026-07-05T00:23:20Z"},{"alias_kind":"pith_short_16","alias_value":"DGG67WW4EMK7544X","created_at":"2026-07-05T00:23:20Z"},{"alias_kind":"pith_short_8","alias_value":"DGG67WW4","created_at":"2026-07-05T00:23:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:DGG67WW4EMK7544XKHZFTT6LM2","target":"record","payload":{"canonical_record":{"source":{"id":"1809.06110","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-09-17T10:18:25Z","cross_cats_sorted":["math.AP","math.MP","math.SP"],"title_canon_sha256":"ee407dfb39f8618bc32cfa127241459f092e6534a7374907e578a44376701782","abstract_canon_sha256":"8c6b13cb36d1c4e52f295efac5e80d153ff4d7ac383e56ea26f6f98dd7bca51e"},"schema_version":"1.0"},"canonical_sha256":"198defdadc2315fef39751f259cfcb66adf67435e08ce4f6f8597acc53956a3d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:23:20.337003Z","signature_b64":"IWWGxQ18Qi7bA7+FgsDGrLns8IuePkP1c6+LCxMGVZyx8nN7ghBf9NVtEsJ/APjsgkEykEe5XqmDyi40WD+fAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"198defdadc2315fef39751f259cfcb66adf67435e08ce4f6f8597acc53956a3d","last_reissued_at":"2026-07-05T00:23:20.336446Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:23:20.336446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.06110","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":"2026-07-05T00:23:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l1D8+p5YmFvsLy/klP3AQxFZtNff4MUCff8BYXy0d4R+wD8lBBkUWhJ4ga4DqKPLNeox8/H1/Kmr2I35MJLqBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:13:32.898409Z"},"content_sha256":"6de4539efecf80664021f5fcc229ea671539e56176ede4ac8c4d054378937cf6","schema_version":"1.0","event_id":"sha256:6de4539efecf80664021f5fcc229ea671539e56176ede4ac8c4d054378937cf6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:DGG67WW4EMK7544XKHZFTT6LM2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compactness of molecular reaction paths in quantum mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Ioannis Anapolitanos, Mathieu Lewin","submitted_at":"2018-09-17T10:18:25Z","abstract_excerpt":"We study isomerizations in quantum mechanics. We consider a neutral molecule composed of N quantum electrons and M classical nuclei and assume that the first eigenvalue of the corresponding N-particle Schr\\\"odinger operator possesses two local minima with respect to the locations of the nuclei. An isomerization is a mountain pass problem between these two local configurations, where one minimizes over all possible paths the highest value of the energy along the paths. Here we state a conjecture about the compactness of min-maxing sequences of such paths, which we then partly solve in the parti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06110","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1809.06110/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":"2026-07-05T00:23:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yjeqLjc/akrVSI4wIkD2Jdc2xQjSGogzpssws7GJla8v7o49EfDDM4vNq6zYp6mdN+dMDwJCUxkZeMskdAwMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:13:32.898796Z"},"content_sha256":"d11644ec9b427717ee9890730c063f8fcd8b29d45ec440837eb13bc815067fdf","schema_version":"1.0","event_id":"sha256:d11644ec9b427717ee9890730c063f8fcd8b29d45ec440837eb13bc815067fdf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DGG67WW4EMK7544XKHZFTT6LM2/bundle.json","state_url":"https://pith.science/pith/DGG67WW4EMK7544XKHZFTT6LM2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DGG67WW4EMK7544XKHZFTT6LM2/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":"2026-08-04T09:13:32Z","links":{"resolver":"https://pith.science/pith/DGG67WW4EMK7544XKHZFTT6LM2","bundle":"https://pith.science/pith/DGG67WW4EMK7544XKHZFTT6LM2/bundle.json","state":"https://pith.science/pith/DGG67WW4EMK7544XKHZFTT6LM2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DGG67WW4EMK7544XKHZFTT6LM2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DGG67WW4EMK7544XKHZFTT6LM2","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":"8c6b13cb36d1c4e52f295efac5e80d153ff4d7ac383e56ea26f6f98dd7bca51e","cross_cats_sorted":["math.AP","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-09-17T10:18:25Z","title_canon_sha256":"ee407dfb39f8618bc32cfa127241459f092e6534a7374907e578a44376701782"},"schema_version":"1.0","source":{"id":"1809.06110","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.06110","created_at":"2026-07-05T00:23:20Z"},{"alias_kind":"arxiv_version","alias_value":"1809.06110v2","created_at":"2026-07-05T00:23:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.06110","created_at":"2026-07-05T00:23:20Z"},{"alias_kind":"pith_short_12","alias_value":"DGG67WW4EMK7","created_at":"2026-07-05T00:23:20Z"},{"alias_kind":"pith_short_16","alias_value":"DGG67WW4EMK7544X","created_at":"2026-07-05T00:23:20Z"},{"alias_kind":"pith_short_8","alias_value":"DGG67WW4","created_at":"2026-07-05T00:23:20Z"}],"graph_snapshots":[{"event_id":"sha256:d11644ec9b427717ee9890730c063f8fcd8b29d45ec440837eb13bc815067fdf","target":"graph","created_at":"2026-07-05T00:23:20Z","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/1809.06110/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study isomerizations in quantum mechanics. We consider a neutral molecule composed of N quantum electrons and M classical nuclei and assume that the first eigenvalue of the corresponding N-particle Schr\\\"odinger operator possesses two local minima with respect to the locations of the nuclei. An isomerization is a mountain pass problem between these two local configurations, where one minimizes over all possible paths the highest value of the energy along the paths. Here we state a conjecture about the compactness of min-maxing sequences of such paths, which we then partly solve in the parti","authors_text":"Ioannis Anapolitanos, Mathieu Lewin","cross_cats":["math.AP","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-09-17T10:18:25Z","title":"Compactness of molecular reaction paths in quantum mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06110","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":"sha256:6de4539efecf80664021f5fcc229ea671539e56176ede4ac8c4d054378937cf6","target":"record","created_at":"2026-07-05T00:23:20Z","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":"8c6b13cb36d1c4e52f295efac5e80d153ff4d7ac383e56ea26f6f98dd7bca51e","cross_cats_sorted":["math.AP","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-09-17T10:18:25Z","title_canon_sha256":"ee407dfb39f8618bc32cfa127241459f092e6534a7374907e578a44376701782"},"schema_version":"1.0","source":{"id":"1809.06110","kind":"arxiv","version":2}},"canonical_sha256":"198defdadc2315fef39751f259cfcb66adf67435e08ce4f6f8597acc53956a3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"198defdadc2315fef39751f259cfcb66adf67435e08ce4f6f8597acc53956a3d","first_computed_at":"2026-07-05T00:23:20.336446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:23:20.336446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IWWGxQ18Qi7bA7+FgsDGrLns8IuePkP1c6+LCxMGVZyx8nN7ghBf9NVtEsJ/APjsgkEykEe5XqmDyi40WD+fAg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:23:20.337003Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.06110","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6de4539efecf80664021f5fcc229ea671539e56176ede4ac8c4d054378937cf6","sha256:d11644ec9b427717ee9890730c063f8fcd8b29d45ec440837eb13bc815067fdf"],"state_sha256":"dcc49b054d2e14fbe7879d075da763ea081c8c649eb505f3fad8184b9f0893b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6c3P2v+hGOHfICHuGnSNxgt7S0wXzD/6KEeNKYuT1NpS8nrX6N3VQePc9uKPa0qqPl0NLgBkMphv9WDHDABiCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T09:13:32.901538Z","bundle_sha256":"a74d763490a3a03c7fa12f4dc754f03f2b5a13e678c4cb93022297b2aff59a32"}}