{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XMAWKLGO6ZPCMJJAWT7DIPO4S4","short_pith_number":"pith:XMAWKLGO","canonical_record":{"source":{"id":"1606.00297","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-01T14:16:51Z","cross_cats_sorted":["math-ph","math.CA","math.MP","math.PR","quant-ph"],"title_canon_sha256":"fca24ddcf2a4dd6482871b924a0e1a3c0dd6141785868c18e36df3b23404e580","abstract_canon_sha256":"49a7a985fd69a0f4cc7f18b4221b411ac6abd2120fb554c633f7afca45e0d3e4"},"schema_version":"1.0"},"canonical_sha256":"bb01652ccef65e262520b4fe343ddc972e39d04e5e20cf342d0929fb3e7742d7","source":{"kind":"arxiv","id":"1606.00297","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00297","created_at":"2026-05-18T01:13:04Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00297v2","created_at":"2026-05-18T01:13:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00297","created_at":"2026-05-18T01:13:04Z"},{"alias_kind":"pith_short_12","alias_value":"XMAWKLGO6ZPC","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XMAWKLGO6ZPCMJJA","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XMAWKLGO","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XMAWKLGO6ZPCMJJAWT7DIPO4S4","target":"record","payload":{"canonical_record":{"source":{"id":"1606.00297","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-01T14:16:51Z","cross_cats_sorted":["math-ph","math.CA","math.MP","math.PR","quant-ph"],"title_canon_sha256":"fca24ddcf2a4dd6482871b924a0e1a3c0dd6141785868c18e36df3b23404e580","abstract_canon_sha256":"49a7a985fd69a0f4cc7f18b4221b411ac6abd2120fb554c633f7afca45e0d3e4"},"schema_version":"1.0"},"canonical_sha256":"bb01652ccef65e262520b4fe343ddc972e39d04e5e20cf342d0929fb3e7742d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:04.387627Z","signature_b64":"yT/j1YMrbxaGZHwOEzf7W9sZ5xOhUC6zeTIJ9GE4hm6zhiCz0MdblN0IjMi3Ae9rey/4CQsX2dHxTdRePTL5DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb01652ccef65e262520b4fe343ddc972e39d04e5e20cf342d0929fb3e7742d7","last_reissued_at":"2026-05-18T01:13:04.387128Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:04.387128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.00297","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":"2026-05-18T01:13:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R9w5OYrxH/4KU2uN1UOQbRfEnvWbsl5V+QtYKrLpazP9T5tGv5XdKgdow9zDJfKJ/JQMcNSg4bGS2Hg42nD/BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:43:59.176871Z"},"content_sha256":"ea267eb923412a275ced9486e3ed42ac685e6d8e88a1a8fb882c6f98866380cf","schema_version":"1.0","event_id":"sha256:ea267eb923412a275ced9486e3ed42ac685e6d8e88a1a8fb882c6f98866380cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XMAWKLGO6ZPCMJJAWT7DIPO4S4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transport and large deviations for Schrodinger operators and Mather measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP","math.PR","quant-ph"],"primary_cat":"math.DS","authors_text":"Artur O. Lopes, P. Thieullen","submitted_at":"2016-06-01T14:16:51Z","abstract_excerpt":"In this mainly survey paper we consider the Lagrangian $ L(x,v) = \\frac{1}{2} \\, |v|^2 - V(x) $, and a closed form $w$ on the torus $ \\mathbb{T}^n $. For the associated Hamiltonian we consider the the Schrodinger operator ${\\bf H}_\\beta=\\, -\\,\\frac{1}{2 \\beta^2} \\, \\Delta +V$ where $\\beta$ is large real parameter. Moreover, for the given form $\\beta\\, w$ we consider the associated twist operator ${\\bf H}_\\beta^w$. We denote by $({\\bf H}_\\beta^w)^*$ the corresponding backward operator. We are interested in the positive eigenfunction $ \\psi_\\beta$ associated to the the eigenvalue $ E_\\beta$ for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00297","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":"2026-05-18T01:13:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NguTTDrcZf+T6EZHVHeRLs14K/sLRV5x5RdY23rajXn5rytIyv+Ar6aErdWJhZS7L1pFdAkgvQt5gsnXbFZNBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:43:59.177234Z"},"content_sha256":"a0e664a5ed273f6bd68ffd73a0da9ce63ec9067a82820ba0acb3a532e18a56f5","schema_version":"1.0","event_id":"sha256:a0e664a5ed273f6bd68ffd73a0da9ce63ec9067a82820ba0acb3a532e18a56f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XMAWKLGO6ZPCMJJAWT7DIPO4S4/bundle.json","state_url":"https://pith.science/pith/XMAWKLGO6ZPCMJJAWT7DIPO4S4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XMAWKLGO6ZPCMJJAWT7DIPO4S4/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":"2026-06-03T14:43:59Z","links":{"resolver":"https://pith.science/pith/XMAWKLGO6ZPCMJJAWT7DIPO4S4","bundle":"https://pith.science/pith/XMAWKLGO6ZPCMJJAWT7DIPO4S4/bundle.json","state":"https://pith.science/pith/XMAWKLGO6ZPCMJJAWT7DIPO4S4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XMAWKLGO6ZPCMJJAWT7DIPO4S4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XMAWKLGO6ZPCMJJAWT7DIPO4S4","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":"49a7a985fd69a0f4cc7f18b4221b411ac6abd2120fb554c633f7afca45e0d3e4","cross_cats_sorted":["math-ph","math.CA","math.MP","math.PR","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-01T14:16:51Z","title_canon_sha256":"fca24ddcf2a4dd6482871b924a0e1a3c0dd6141785868c18e36df3b23404e580"},"schema_version":"1.0","source":{"id":"1606.00297","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00297","created_at":"2026-05-18T01:13:04Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00297v2","created_at":"2026-05-18T01:13:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00297","created_at":"2026-05-18T01:13:04Z"},{"alias_kind":"pith_short_12","alias_value":"XMAWKLGO6ZPC","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XMAWKLGO6ZPCMJJA","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XMAWKLGO","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:a0e664a5ed273f6bd68ffd73a0da9ce63ec9067a82820ba0acb3a532e18a56f5","target":"graph","created_at":"2026-05-18T01:13:04Z","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":"In this mainly survey paper we consider the Lagrangian $ L(x,v) = \\frac{1}{2} \\, |v|^2 - V(x) $, and a closed form $w$ on the torus $ \\mathbb{T}^n $. For the associated Hamiltonian we consider the the Schrodinger operator ${\\bf H}_\\beta=\\, -\\,\\frac{1}{2 \\beta^2} \\, \\Delta +V$ where $\\beta$ is large real parameter. Moreover, for the given form $\\beta\\, w$ we consider the associated twist operator ${\\bf H}_\\beta^w$. We denote by $({\\bf H}_\\beta^w)^*$ the corresponding backward operator. We are interested in the positive eigenfunction $ \\psi_\\beta$ associated to the the eigenvalue $ E_\\beta$ for ","authors_text":"Artur O. Lopes, P. Thieullen","cross_cats":["math-ph","math.CA","math.MP","math.PR","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-01T14:16:51Z","title":"Transport and large deviations for Schrodinger operators and Mather measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00297","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:ea267eb923412a275ced9486e3ed42ac685e6d8e88a1a8fb882c6f98866380cf","target":"record","created_at":"2026-05-18T01:13:04Z","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":"49a7a985fd69a0f4cc7f18b4221b411ac6abd2120fb554c633f7afca45e0d3e4","cross_cats_sorted":["math-ph","math.CA","math.MP","math.PR","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-01T14:16:51Z","title_canon_sha256":"fca24ddcf2a4dd6482871b924a0e1a3c0dd6141785868c18e36df3b23404e580"},"schema_version":"1.0","source":{"id":"1606.00297","kind":"arxiv","version":2}},"canonical_sha256":"bb01652ccef65e262520b4fe343ddc972e39d04e5e20cf342d0929fb3e7742d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb01652ccef65e262520b4fe343ddc972e39d04e5e20cf342d0929fb3e7742d7","first_computed_at":"2026-05-18T01:13:04.387128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:04.387128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yT/j1YMrbxaGZHwOEzf7W9sZ5xOhUC6zeTIJ9GE4hm6zhiCz0MdblN0IjMi3Ae9rey/4CQsX2dHxTdRePTL5DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:04.387627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.00297","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea267eb923412a275ced9486e3ed42ac685e6d8e88a1a8fb882c6f98866380cf","sha256:a0e664a5ed273f6bd68ffd73a0da9ce63ec9067a82820ba0acb3a532e18a56f5"],"state_sha256":"129587383cc65dc9741067839d06f5e1ca93186e9e77b9e7a5cb82c7b22aa917"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AV/0Q3RPUdDNumShQg0AarybRtkLEI7SSo7tPsXewRQkt+J8UcafQ8U5AstGAYHAunQsKCIRX9z/StqOGZsjDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T14:43:59.179297Z","bundle_sha256":"1c65514484197a1c71c66faa1114ce21c65c51fc516ebc56ac2a0c709f0cb94c"}}