{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:YDD7UAHBABLVRAZPCAYNSNPUHN","short_pith_number":"pith:YDD7UAHB","schema_version":"1.0","canonical_sha256":"c0c7fa00e1005758832f1030d935f43b4f56a08742958c90b1016b822838a919","source":{"kind":"arxiv","id":"1908.10872","version":1},"attestation_state":"computed","paper":{"title":"A Measure for Quantum Paths, Gravity and Spacetime Microstructure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"T. Padmanabhan","submitted_at":"2019-08-28T18:00:04Z","abstract_excerpt":"The number of classical paths of a given length, connecting any two events in a (pseudo) Riemannian spacetime is, of course, infinite. It is, however, possible to define a useful, finite, measure $N(x_2,x_1;\\sigma)$ for the effective number of quantum paths [of length $\\sigma$ connecting two events $(x_1,x_2)$] in an arbitrary spacetime. When $x_2=x_1$, this reduces to $C(x,\\sigma)$ giving the measure for closed quantum loops of length $\\sigma$ containing an event $x$. Both $N(x_2,x_1;\\sigma)$ and $C(x,\\sigma)$ are well-defined and depend only on the geometry of the spacetime. Various other ph"},"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":"1908.10872","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-08-28T18:00:04Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"7583a4438b59ed7bbe4e35fb9207570c1c19554790e3e5492c1f83c5db651bf0","abstract_canon_sha256":"141902c78c2b9e22e76ef27ad3e8c062020a4608316a0333395d1cc8e5e576f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:00:28.305146Z","signature_b64":"ORD1F8UvSdRW1CkRLk8zYVMwp2/81J2GVXpLmohMC86u3wQt3+AqypUeKEipOMVtL1WIMsrdSEN2fEFTL8DCAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0c7fa00e1005758832f1030d935f43b4f56a08742958c90b1016b822838a919","last_reissued_at":"2026-07-05T00:00:28.304653Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:00:28.304653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Measure for Quantum Paths, Gravity and Spacetime Microstructure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"T. Padmanabhan","submitted_at":"2019-08-28T18:00:04Z","abstract_excerpt":"The number of classical paths of a given length, connecting any two events in a (pseudo) Riemannian spacetime is, of course, infinite. It is, however, possible to define a useful, finite, measure $N(x_2,x_1;\\sigma)$ for the effective number of quantum paths [of length $\\sigma$ connecting two events $(x_1,x_2)$] in an arbitrary spacetime. When $x_2=x_1$, this reduces to $C(x,\\sigma)$ giving the measure for closed quantum loops of length $\\sigma$ containing an event $x$. Both $N(x_2,x_1;\\sigma)$ and $C(x,\\sigma)$ are well-defined and depend only on the geometry of the spacetime. Various other ph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.10872","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/1908.10872/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":"1908.10872","created_at":"2026-07-05T00:00:28.304710+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.10872v1","created_at":"2026-07-05T00:00:28.304710+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.10872","created_at":"2026-07-05T00:00:28.304710+00:00"},{"alias_kind":"pith_short_12","alias_value":"YDD7UAHBABLV","created_at":"2026-07-05T00:00:28.304710+00:00"},{"alias_kind":"pith_short_16","alias_value":"YDD7UAHBABLVRAZP","created_at":"2026-07-05T00:00:28.304710+00:00"},{"alias_kind":"pith_short_8","alias_value":"YDD7UAHB","created_at":"2026-07-05T00:00:28.304710+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/YDD7UAHBABLVRAZPCAYNSNPUHN","json":"https://pith.science/pith/YDD7UAHBABLVRAZPCAYNSNPUHN.json","graph_json":"https://pith.science/api/pith-number/YDD7UAHBABLVRAZPCAYNSNPUHN/graph.json","events_json":"https://pith.science/api/pith-number/YDD7UAHBABLVRAZPCAYNSNPUHN/events.json","paper":"https://pith.science/paper/YDD7UAHB"},"agent_actions":{"view_html":"https://pith.science/pith/YDD7UAHBABLVRAZPCAYNSNPUHN","download_json":"https://pith.science/pith/YDD7UAHBABLVRAZPCAYNSNPUHN.json","view_paper":"https://pith.science/paper/YDD7UAHB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.10872&json=true","fetch_graph":"https://pith.science/api/pith-number/YDD7UAHBABLVRAZPCAYNSNPUHN/graph.json","fetch_events":"https://pith.science/api/pith-number/YDD7UAHBABLVRAZPCAYNSNPUHN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YDD7UAHBABLVRAZPCAYNSNPUHN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YDD7UAHBABLVRAZPCAYNSNPUHN/action/storage_attestation","attest_author":"https://pith.science/pith/YDD7UAHBABLVRAZPCAYNSNPUHN/action/author_attestation","sign_citation":"https://pith.science/pith/YDD7UAHBABLVRAZPCAYNSNPUHN/action/citation_signature","submit_replication":"https://pith.science/pith/YDD7UAHBABLVRAZPCAYNSNPUHN/action/replication_record"}},"created_at":"2026-07-05T00:00:28.304710+00:00","updated_at":"2026-07-05T00:00:28.304710+00:00"}