{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:NYWGZT5WU5FHUXOBZNRZC64CL4","short_pith_number":"pith:NYWGZT5W","canonical_record":{"source":{"id":"2607.21509","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-07-23T16:54:54Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"7eb06baacac1676a50ce30e37ea378ecdff304595a534a983ea3e51cff26d965","abstract_canon_sha256":"8159f38649d49f6074a9bf8e4cc3cd826ae4ec9e640e7c90ee5202d01fe02977"},"schema_version":"1.0"},"canonical_sha256":"6e2c6ccfb6a74a7a5dc1cb63917b825f15243ffac72d1b6f8854c7c9f1d6a617","source":{"kind":"arxiv","id":"2607.21509","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.21509","created_at":"2026-07-24T01:24:36Z"},{"alias_kind":"arxiv_version","alias_value":"2607.21509v1","created_at":"2026-07-24T01:24:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.21509","created_at":"2026-07-24T01:24:36Z"},{"alias_kind":"pith_short_12","alias_value":"NYWGZT5WU5FH","created_at":"2026-07-24T01:24:36Z"},{"alias_kind":"pith_short_16","alias_value":"NYWGZT5WU5FHUXOB","created_at":"2026-07-24T01:24:36Z"},{"alias_kind":"pith_short_8","alias_value":"NYWGZT5W","created_at":"2026-07-24T01:24:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:NYWGZT5WU5FHUXOBZNRZC64CL4","target":"record","payload":{"canonical_record":{"source":{"id":"2607.21509","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-07-23T16:54:54Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"7eb06baacac1676a50ce30e37ea378ecdff304595a534a983ea3e51cff26d965","abstract_canon_sha256":"8159f38649d49f6074a9bf8e4cc3cd826ae4ec9e640e7c90ee5202d01fe02977"},"schema_version":"1.0"},"canonical_sha256":"6e2c6ccfb6a74a7a5dc1cb63917b825f15243ffac72d1b6f8854c7c9f1d6a617","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-24T01:24:36.885676Z","signature_b64":"kZS72U6KjSuFg7ezhUGI6isqPffShSKUBxmMX8A2MErvJZergNCSoqGCwhWxaj9ASB1Hze46Pmh3qSIpNprdDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e2c6ccfb6a74a7a5dc1cb63917b825f15243ffac72d1b6f8854c7c9f1d6a617","last_reissued_at":"2026-07-24T01:24:36.884862Z","signature_status":"signed_v1","first_computed_at":"2026-07-24T01:24:36.884862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.21509","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-24T01:24:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"olVOZUUhUQQZkPQ3OLTO/tkThtv2EK2O+i2qOwMeYzsGBTSioYydiDhmo6V9RGHR2TDk5Bf9YHvrstuEecKLDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T15:38:23.809226Z"},"content_sha256":"65accfb410185eb755416a377f2162d9444a18f6001f2eabe850ec24184c02fd","schema_version":"1.0","event_id":"sha256:65accfb410185eb755416a377f2162d9444a18f6001f2eabe850ec24184c02fd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:NYWGZT5WU5FHUXOBZNRZC64CL4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Aspects of Closed Matricial Worlds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Dionysios Anninos, Samuel Brian","submitted_at":"2026-07-23T16:54:54Z","abstract_excerpt":"We investigate the Hilbert space structure for simple theories of gravity with $\\Lambda>0$ on closed spatial sections. Our motivation ties to the presence of gravitational saddles in four-dimensional $\\Lambda>0$ Einstein-Maxwell theory with $S^2\\times \\Sigma_h$ topology, where $\\Sigma_h$ is a genus-$h$ Riemann surface. Here, as a concrete starting point, the problem is explored for two-dimensional $\\Lambda>0$ quantum gravity. We revisit and elaborate on exact results in the matrix model literature. We study gravitational wavefunctions from both the perspective of the Wheeler-DeWitt equation an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.21509","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/2607.21509/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-24T01:24:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/1B8hZZ+ibmLWTuLcpYQEkP05J+/knm6FwH1W2tS1m5mpeJaAFXy9MObmS+iuVLhnZl0AJHmo7/HXRolIFHxDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T15:38:23.809810Z"},"content_sha256":"ebcae09af7149f96bdf843d5109aa07582cfaf985bea3e95544f16444f742fd8","schema_version":"1.0","event_id":"sha256:ebcae09af7149f96bdf843d5109aa07582cfaf985bea3e95544f16444f742fd8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NYWGZT5WU5FHUXOBZNRZC64CL4/bundle.json","state_url":"https://pith.science/pith/NYWGZT5WU5FHUXOBZNRZC64CL4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NYWGZT5WU5FHUXOBZNRZC64CL4/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":"2026-08-05T15:38:23Z","links":{"resolver":"https://pith.science/pith/NYWGZT5WU5FHUXOBZNRZC64CL4","bundle":"https://pith.science/pith/NYWGZT5WU5FHUXOBZNRZC64CL4/bundle.json","state":"https://pith.science/pith/NYWGZT5WU5FHUXOBZNRZC64CL4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NYWGZT5WU5FHUXOBZNRZC64CL4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:NYWGZT5WU5FHUXOBZNRZC64CL4","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":"8159f38649d49f6074a9bf8e4cc3cd826ae4ec9e640e7c90ee5202d01fe02977","cross_cats_sorted":["gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-07-23T16:54:54Z","title_canon_sha256":"7eb06baacac1676a50ce30e37ea378ecdff304595a534a983ea3e51cff26d965"},"schema_version":"1.0","source":{"id":"2607.21509","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.21509","created_at":"2026-07-24T01:24:36Z"},{"alias_kind":"arxiv_version","alias_value":"2607.21509v1","created_at":"2026-07-24T01:24:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.21509","created_at":"2026-07-24T01:24:36Z"},{"alias_kind":"pith_short_12","alias_value":"NYWGZT5WU5FH","created_at":"2026-07-24T01:24:36Z"},{"alias_kind":"pith_short_16","alias_value":"NYWGZT5WU5FHUXOB","created_at":"2026-07-24T01:24:36Z"},{"alias_kind":"pith_short_8","alias_value":"NYWGZT5W","created_at":"2026-07-24T01:24:36Z"}],"graph_snapshots":[{"event_id":"sha256:ebcae09af7149f96bdf843d5109aa07582cfaf985bea3e95544f16444f742fd8","target":"graph","created_at":"2026-07-24T01:24:36Z","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/2607.21509/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the Hilbert space structure for simple theories of gravity with $\\Lambda>0$ on closed spatial sections. Our motivation ties to the presence of gravitational saddles in four-dimensional $\\Lambda>0$ Einstein-Maxwell theory with $S^2\\times \\Sigma_h$ topology, where $\\Sigma_h$ is a genus-$h$ Riemann surface. Here, as a concrete starting point, the problem is explored for two-dimensional $\\Lambda>0$ quantum gravity. We revisit and elaborate on exact results in the matrix model literature. We study gravitational wavefunctions from both the perspective of the Wheeler-DeWitt equation an","authors_text":"Dionysios Anninos, Samuel Brian","cross_cats":["gr-qc"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-07-23T16:54:54Z","title":"Aspects of Closed Matricial Worlds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.21509","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":"sha256:65accfb410185eb755416a377f2162d9444a18f6001f2eabe850ec24184c02fd","target":"record","created_at":"2026-07-24T01:24:36Z","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":"8159f38649d49f6074a9bf8e4cc3cd826ae4ec9e640e7c90ee5202d01fe02977","cross_cats_sorted":["gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2026-07-23T16:54:54Z","title_canon_sha256":"7eb06baacac1676a50ce30e37ea378ecdff304595a534a983ea3e51cff26d965"},"schema_version":"1.0","source":{"id":"2607.21509","kind":"arxiv","version":1}},"canonical_sha256":"6e2c6ccfb6a74a7a5dc1cb63917b825f15243ffac72d1b6f8854c7c9f1d6a617","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e2c6ccfb6a74a7a5dc1cb63917b825f15243ffac72d1b6f8854c7c9f1d6a617","first_computed_at":"2026-07-24T01:24:36.884862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-24T01:24:36.884862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kZS72U6KjSuFg7ezhUGI6isqPffShSKUBxmMX8A2MErvJZergNCSoqGCwhWxaj9ASB1Hze46Pmh3qSIpNprdDw==","signature_status":"signed_v1","signed_at":"2026-07-24T01:24:36.885676Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.21509","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65accfb410185eb755416a377f2162d9444a18f6001f2eabe850ec24184c02fd","sha256:ebcae09af7149f96bdf843d5109aa07582cfaf985bea3e95544f16444f742fd8"],"state_sha256":"ff352c57a868215ece170c2ef873e951d6ebd818e54d240f3dbcb8f23e0d00c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7lIx4NOK0qGgp57Sr8vqsx37m18h/UYPL6Xp0Im/xmOPmWw5d+o+CmU79I8PH9TVEQk7EQXeoG2gGkpfiKJLCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T15:38:23.813215Z","bundle_sha256":"22f033757e3491c2ecc9490d31e73dbc4fcab25d14a0a26684d92c356a033dac"}}