{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:YRDPRGULIWNZS7VVV32YQ2OXFK","short_pith_number":"pith:YRDPRGUL","schema_version":"1.0","canonical_sha256":"c446f89a8b459b997eb5aef58869d72aaf4533b118a1570d7a26dfe148db7545","source":{"kind":"arxiv","id":"2606.01296","version":1},"attestation_state":"computed","paper":{"title":"Notes on Wasserstein distance and wormholes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Ville Keranen","submitted_at":"2026-05-31T15:33:47Z","abstract_excerpt":"We develop the Boltzmann--Wasserstein (BW) distance, a temperature-dependent metric on the space of quantum theories defined as the optimal $W_2$ distance between Boltzmann-weighted energy spectra. For semiclassical theories differing by a small entropy shift, the normalised BW distance collapses to a squared horizon-area comparator, $\\tilde{\\mathcal{W}}^2 \\approx (\\delta A/4G)^2/8$, with the two areas evaluated at equal energy. When the Hamiltonians of the theories differ by an operator $V$, then the BW distance equals a time-averaged thermal two-point function of $V$; for primary perturbatio"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.01296","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-05-31T15:33:47Z","cross_cats_sorted":[],"title_canon_sha256":"68d24a607dcff2d6dc6ebd465480e8330b0ce3d3a89620293fb641be2c6d2354","abstract_canon_sha256":"717763002e2af2b36b6ad1c3dc27785e5c7a3afb3a90684143b6051952057384"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:29.351868Z","signature_b64":"UN9jfvSC9mwGyRbGImLAnnatadyoxHved+b5fD2Kzzyzqlns4ou3OKO+KnkI+XtNns47uu5UjYwGsYIqsOAmAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c446f89a8b459b997eb5aef58869d72aaf4533b118a1570d7a26dfe148db7545","last_reissued_at":"2026-06-02T02:04:29.351484Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:29.351484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Notes on Wasserstein distance and wormholes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Ville Keranen","submitted_at":"2026-05-31T15:33:47Z","abstract_excerpt":"We develop the Boltzmann--Wasserstein (BW) distance, a temperature-dependent metric on the space of quantum theories defined as the optimal $W_2$ distance between Boltzmann-weighted energy spectra. For semiclassical theories differing by a small entropy shift, the normalised BW distance collapses to a squared horizon-area comparator, $\\tilde{\\mathcal{W}}^2 \\approx (\\delta A/4G)^2/8$, with the two areas evaluated at equal energy. When the Hamiltonians of the theories differ by an operator $V$, then the BW distance equals a time-averaged thermal two-point function of $V$; for primary perturbatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01296","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/2606.01296/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.01296","created_at":"2026-06-02T02:04:29.351545+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.01296v1","created_at":"2026-06-02T02:04:29.351545+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01296","created_at":"2026-06-02T02:04:29.351545+00:00"},{"alias_kind":"pith_short_12","alias_value":"YRDPRGULIWNZ","created_at":"2026-06-02T02:04:29.351545+00:00"},{"alias_kind":"pith_short_16","alias_value":"YRDPRGULIWNZS7VV","created_at":"2026-06-02T02:04:29.351545+00:00"},{"alias_kind":"pith_short_8","alias_value":"YRDPRGUL","created_at":"2026-06-02T02:04:29.351545+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YRDPRGULIWNZS7VVV32YQ2OXFK","json":"https://pith.science/pith/YRDPRGULIWNZS7VVV32YQ2OXFK.json","graph_json":"https://pith.science/api/pith-number/YRDPRGULIWNZS7VVV32YQ2OXFK/graph.json","events_json":"https://pith.science/api/pith-number/YRDPRGULIWNZS7VVV32YQ2OXFK/events.json","paper":"https://pith.science/paper/YRDPRGUL"},"agent_actions":{"view_html":"https://pith.science/pith/YRDPRGULIWNZS7VVV32YQ2OXFK","download_json":"https://pith.science/pith/YRDPRGULIWNZS7VVV32YQ2OXFK.json","view_paper":"https://pith.science/paper/YRDPRGUL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.01296&json=true","fetch_graph":"https://pith.science/api/pith-number/YRDPRGULIWNZS7VVV32YQ2OXFK/graph.json","fetch_events":"https://pith.science/api/pith-number/YRDPRGULIWNZS7VVV32YQ2OXFK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YRDPRGULIWNZS7VVV32YQ2OXFK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YRDPRGULIWNZS7VVV32YQ2OXFK/action/storage_attestation","attest_author":"https://pith.science/pith/YRDPRGULIWNZS7VVV32YQ2OXFK/action/author_attestation","sign_citation":"https://pith.science/pith/YRDPRGULIWNZS7VVV32YQ2OXFK/action/citation_signature","submit_replication":"https://pith.science/pith/YRDPRGULIWNZS7VVV32YQ2OXFK/action/replication_record"}},"created_at":"2026-06-02T02:04:29.351545+00:00","updated_at":"2026-06-02T02:04:29.351545+00:00"}