{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:ABNFNEYYERQFRA2XSLPIQWG57Y","short_pith_number":"pith:ABNFNEYY","schema_version":"1.0","canonical_sha256":"005a569318246058835792de8858ddfe3dd81c2c1a234411e2ea664555131393","source":{"kind":"arxiv","id":"2606.21585","version":1},"attestation_state":"computed","paper":{"title":"The Cost Geometry of Belief: finite-resource inference under noisy observation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","math.DG","math.IT","math.ST","stat.TH"],"primary_cat":"cs.LG","authors_text":"Laurent Caraffa","submitted_at":"2026-06-19T16:41:28Z","abstract_excerpt":"We equip the space of beliefs with a cost geometry (what it costs to pass from one belief to another): optimal transport in Wasserstein space, reweighted conformally by Fisher information (the price of the precision at stake), distinct from the Fisher-Rao metric. In the setting we consider, a finite machine maintains a digital twin of a system; observing the territory through finite, noisy sensors, we model its coherent output as a belief: a probability density over states, the Bayes posterior. Certainty (the perfect twin) is denied twice, by observation and by physics, both read off the Fishe"},"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":"2606.21585","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-19T16:41:28Z","cross_cats_sorted":["cs.IT","math.DG","math.IT","math.ST","stat.TH"],"title_canon_sha256":"cfcf21ad78861cd77b66e7778c24b691ec4aeb3bb342d895975f31149dc12e43","abstract_canon_sha256":"69e840130d258885e6912c2bd4de96832b06469208d806a405136585fd959bd6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T01:13:15.394488Z","signature_b64":"yupTy6esoukbt8x+OjDLCiq/Yra/5j1P6x7k5SJ/VVwOH1SVKejsB8HLyL8psDwVZwHfMaewYQK8KZ5lhuWxAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"005a569318246058835792de8858ddfe3dd81c2c1a234411e2ea664555131393","last_reissued_at":"2026-06-23T01:13:15.393995Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T01:13:15.393995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Cost Geometry of Belief: finite-resource inference under noisy observation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","math.DG","math.IT","math.ST","stat.TH"],"primary_cat":"cs.LG","authors_text":"Laurent Caraffa","submitted_at":"2026-06-19T16:41:28Z","abstract_excerpt":"We equip the space of beliefs with a cost geometry (what it costs to pass from one belief to another): optimal transport in Wasserstein space, reweighted conformally by Fisher information (the price of the precision at stake), distinct from the Fisher-Rao metric. In the setting we consider, a finite machine maintains a digital twin of a system; observing the territory through finite, noisy sensors, we model its coherent output as a belief: a probability density over states, the Bayes posterior. Certainty (the perfect twin) is denied twice, by observation and by physics, both read off the Fishe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21585","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/2606.21585/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":"2606.21585","created_at":"2026-06-23T01:13:15.394063+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.21585v1","created_at":"2026-06-23T01:13:15.394063+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.21585","created_at":"2026-06-23T01:13:15.394063+00:00"},{"alias_kind":"pith_short_12","alias_value":"ABNFNEYYERQF","created_at":"2026-06-23T01:13:15.394063+00:00"},{"alias_kind":"pith_short_16","alias_value":"ABNFNEYYERQFRA2X","created_at":"2026-06-23T01:13:15.394063+00:00"},{"alias_kind":"pith_short_8","alias_value":"ABNFNEYY","created_at":"2026-06-23T01:13:15.394063+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/ABNFNEYYERQFRA2XSLPIQWG57Y","json":"https://pith.science/pith/ABNFNEYYERQFRA2XSLPIQWG57Y.json","graph_json":"https://pith.science/api/pith-number/ABNFNEYYERQFRA2XSLPIQWG57Y/graph.json","events_json":"https://pith.science/api/pith-number/ABNFNEYYERQFRA2XSLPIQWG57Y/events.json","paper":"https://pith.science/paper/ABNFNEYY"},"agent_actions":{"view_html":"https://pith.science/pith/ABNFNEYYERQFRA2XSLPIQWG57Y","download_json":"https://pith.science/pith/ABNFNEYYERQFRA2XSLPIQWG57Y.json","view_paper":"https://pith.science/paper/ABNFNEYY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.21585&json=true","fetch_graph":"https://pith.science/api/pith-number/ABNFNEYYERQFRA2XSLPIQWG57Y/graph.json","fetch_events":"https://pith.science/api/pith-number/ABNFNEYYERQFRA2XSLPIQWG57Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ABNFNEYYERQFRA2XSLPIQWG57Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ABNFNEYYERQFRA2XSLPIQWG57Y/action/storage_attestation","attest_author":"https://pith.science/pith/ABNFNEYYERQFRA2XSLPIQWG57Y/action/author_attestation","sign_citation":"https://pith.science/pith/ABNFNEYYERQFRA2XSLPIQWG57Y/action/citation_signature","submit_replication":"https://pith.science/pith/ABNFNEYYERQFRA2XSLPIQWG57Y/action/replication_record"}},"created_at":"2026-06-23T01:13:15.394063+00:00","updated_at":"2026-06-23T01:13:15.394063+00:00"}