{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:MEADF4X4LJD3YCM52B7G6M63V2","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"65b0bc9473c8ab54952ffbb9e52530e5635d64dda19f6c06ad0596746e8228d2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.gen-ph","submitted_at":"2026-07-30T07:14:50Z","title_canon_sha256":"54fee1623a0703e1a7b643aa20716936a9fac3976b1f34040c830a35c3980751"},"schema_version":"1.0","source":{"id":"2607.28690","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.28690","created_at":"2026-08-03T00:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"2607.28690v1","created_at":"2026-08-03T00:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28690","created_at":"2026-08-03T00:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"MEADF4X4LJD3","created_at":"2026-08-03T00:12:11Z"},{"alias_kind":"pith_short_16","alias_value":"MEADF4X4LJD3YCM5","created_at":"2026-08-03T00:12:11Z"},{"alias_kind":"pith_short_8","alias_value":"MEADF4X4","created_at":"2026-08-03T00:12:11Z"}],"graph_snapshots":[{"event_id":"sha256:6fb3b666f386830a7be16bdf681c53b009418aa3f71743952be6aea989218361","target":"graph","created_at":"2026-08-03T00:12:11Z","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/2607.28690/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a geometric framework based on metric--measure spaces $(M,g,f)$, where the function $f$ defines a deformation of the Riemannian measure motivated by Perelman's formulation of Ricci flow. Within this setting, we introduce measure-weighted hypersurfaces and associated geometric functionals, and derive modified extremality conditions for codimension-one and codimension-two submanifolds.\n  These conditions provide intrinsic geometric analogues of extremal surface equations, arising solely from the metric--measure structure and independent of holographic duality or quantum field theoreti","authors_text":"Rohit Dhormare","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.gen-ph","submitted_at":"2026-07-30T07:14:50Z","title":"Metric--Measure Geometry and Geometric Analogues of Holographic Extremal Surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28690","kind":"arxiv","version":1},"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":"sha256:8208b7b9d6a98969f0435ef1522d781fd3109e4e4e81678788eb7163286aa439","target":"record","created_at":"2026-08-03T00:12:11Z","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":"65b0bc9473c8ab54952ffbb9e52530e5635d64dda19f6c06ad0596746e8228d2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.gen-ph","submitted_at":"2026-07-30T07:14:50Z","title_canon_sha256":"54fee1623a0703e1a7b643aa20716936a9fac3976b1f34040c830a35c3980751"},"schema_version":"1.0","source":{"id":"2607.28690","kind":"arxiv","version":1}},"canonical_sha256":"610032f2fc5a47bc099dd07e6f33dbae902689a25091d684a0811c495b8d355d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"610032f2fc5a47bc099dd07e6f33dbae902689a25091d684a0811c495b8d355d","first_computed_at":"2026-08-03T00:12:11.160070Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-03T00:12:11.160070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JlTv+P1LwMYId2lYpE5vATyqpu2Q7W8jsksUfFBmAtHFU8CdpcqJZAG7o/MAFb7yhRaHf5zUyITbJNfUkJgVAQ==","signature_status":"signed_v1","signed_at":"2026-08-03T00:12:11.162263Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.28690","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8208b7b9d6a98969f0435ef1522d781fd3109e4e4e81678788eb7163286aa439","sha256:6fb3b666f386830a7be16bdf681c53b009418aa3f71743952be6aea989218361","sha256:f18edc8a7a5729e1cb08ffe05cacbeb62bfcc18ce48d99f40f3a5f842ace7ea6"],"state_sha256":"f40f834ee024c7930d0dec0cc4a572fc313c9804126018f45c7d05298e3391e1"}