{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1993:NSZ3QOUM2I5N7WE5BVP5XT5EV2","short_pith_number":"pith:NSZ3QOUM","canonical_record":{"source":{"id":"hep-th/9307065","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1993-07-09T13:16:38Z","cross_cats_sorted":[],"title_canon_sha256":"1ce668b406a9057de36f5b2070e720c539c9f39165683b4f5aae626fe6d9fd6d","abstract_canon_sha256":"2deb0d46d7a4556e4bdb51438116271cf50872fbaa1f6abbf974ae97ab450520"},"schema_version":"1.0"},"canonical_sha256":"6cb3b83a8cd23adfd89d0d5fdbcfa4aeae0f9fe36961087a7102536ac8010267","source":{"kind":"arxiv","id":"hep-th/9307065","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9307065","created_at":"2026-07-04T14:32:37Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9307065v1","created_at":"2026-07-04T14:32:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9307065","created_at":"2026-07-04T14:32:37Z"},{"alias_kind":"pith_short_12","alias_value":"NSZ3QOUM2I5N","created_at":"2026-07-04T14:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"NSZ3QOUM2I5N7WE5","created_at":"2026-07-04T14:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"NSZ3QOUM","created_at":"2026-07-04T14:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1993:NSZ3QOUM2I5N7WE5BVP5XT5EV2","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9307065","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1993-07-09T13:16:38Z","cross_cats_sorted":[],"title_canon_sha256":"1ce668b406a9057de36f5b2070e720c539c9f39165683b4f5aae626fe6d9fd6d","abstract_canon_sha256":"2deb0d46d7a4556e4bdb51438116271cf50872fbaa1f6abbf974ae97ab450520"},"schema_version":"1.0"},"canonical_sha256":"6cb3b83a8cd23adfd89d0d5fdbcfa4aeae0f9fe36961087a7102536ac8010267","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:32:37.684400Z","signature_b64":"vIu6Axxo93vIMnv1Mmjbmht6E0Q2rDax2ZQ3jEzKdoSysqGyeIz29pLtpS6XKgL611jV8Amu/YskjP2MOFQzDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cb3b83a8cd23adfd89d0d5fdbcfa4aeae0f9fe36961087a7102536ac8010267","last_reissued_at":"2026-07-04T14:32:37.683997Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:32:37.683997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9307065","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":"2026-07-04T14:32:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0mu0Nvc493LJn0Q1Bt4LltqYdPS8wTNhvvI/ZI1gAbeUb0SLtPzODEhJIt46KkD4brmIFfyO0RIdHHAUI1K/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T18:44:58.138956Z"},"content_sha256":"04a677ef391b0d2074a416c8c5dda43fc8cf1a522b7709e7b9266bef0e2b45f5","schema_version":"1.0","event_id":"sha256:04a677ef391b0d2074a416c8c5dda43fc8cf1a522b7709e7b9266bef0e2b45f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1993:NSZ3QOUM2I5N7WE5BVP5XT5EV2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Renormalization Group Approach to Discretized Gravity","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"C. Itoi, N. Sakai, S. Higuchi, S. Nishigaki","submitted_at":"1993-07-09T13:16:38Z","abstract_excerpt":"We summarize our renormalization group approach for the vector model as well as the matrix model which are the discretized quantum gravity in one- and two-dimensional spacetime. A difference equation is obtained which relates free energies for neighboring values of $N$. The reparametrization freedom in field space is formulated by means of the loop equation. The reparametrization identities reduce the flow in the infinite dimensional coupling constant space to that in finite dimensions. The matrix model gives a nonlinear differential equation as an effective renormalization group equation. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9307065","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/hep-th/9307065/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":"2026-07-04T14:32:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AqHe9uCBooi4qeQA/QlI1Wdo2TjcteuxwdEw7R7KmkezcJXkWarHY73ErgeGiluv6hq4YADtw1HTNsfHpir7Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T18:44:58.139341Z"},"content_sha256":"368a6ba5e54466bd5e527313a0ceccdc17d2968088ffb428869fbc837121f19b","schema_version":"1.0","event_id":"sha256:368a6ba5e54466bd5e527313a0ceccdc17d2968088ffb428869fbc837121f19b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NSZ3QOUM2I5N7WE5BVP5XT5EV2/bundle.json","state_url":"https://pith.science/pith/NSZ3QOUM2I5N7WE5BVP5XT5EV2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NSZ3QOUM2I5N7WE5BVP5XT5EV2/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":"2026-07-06T18:44:58Z","links":{"resolver":"https://pith.science/pith/NSZ3QOUM2I5N7WE5BVP5XT5EV2","bundle":"https://pith.science/pith/NSZ3QOUM2I5N7WE5BVP5XT5EV2/bundle.json","state":"https://pith.science/pith/NSZ3QOUM2I5N7WE5BVP5XT5EV2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NSZ3QOUM2I5N7WE5BVP5XT5EV2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:NSZ3QOUM2I5N7WE5BVP5XT5EV2","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":"2deb0d46d7a4556e4bdb51438116271cf50872fbaa1f6abbf974ae97ab450520","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1993-07-09T13:16:38Z","title_canon_sha256":"1ce668b406a9057de36f5b2070e720c539c9f39165683b4f5aae626fe6d9fd6d"},"schema_version":"1.0","source":{"id":"hep-th/9307065","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9307065","created_at":"2026-07-04T14:32:37Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9307065v1","created_at":"2026-07-04T14:32:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9307065","created_at":"2026-07-04T14:32:37Z"},{"alias_kind":"pith_short_12","alias_value":"NSZ3QOUM2I5N","created_at":"2026-07-04T14:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"NSZ3QOUM2I5N7WE5","created_at":"2026-07-04T14:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"NSZ3QOUM","created_at":"2026-07-04T14:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:368a6ba5e54466bd5e527313a0ceccdc17d2968088ffb428869fbc837121f19b","target":"graph","created_at":"2026-07-04T14:32:37Z","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/hep-th/9307065/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We summarize our renormalization group approach for the vector model as well as the matrix model which are the discretized quantum gravity in one- and two-dimensional spacetime. A difference equation is obtained which relates free energies for neighboring values of $N$. The reparametrization freedom in field space is formulated by means of the loop equation. The reparametrization identities reduce the flow in the infinite dimensional coupling constant space to that in finite dimensions. The matrix model gives a nonlinear differential equation as an effective renormalization group equation. The","authors_text":"C. Itoi, N. Sakai, S. Higuchi, S. Nishigaki","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1993-07-09T13:16:38Z","title":"Renormalization Group Approach to Discretized Gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9307065","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":"sha256:04a677ef391b0d2074a416c8c5dda43fc8cf1a522b7709e7b9266bef0e2b45f5","target":"record","created_at":"2026-07-04T14:32:37Z","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":"2deb0d46d7a4556e4bdb51438116271cf50872fbaa1f6abbf974ae97ab450520","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1993-07-09T13:16:38Z","title_canon_sha256":"1ce668b406a9057de36f5b2070e720c539c9f39165683b4f5aae626fe6d9fd6d"},"schema_version":"1.0","source":{"id":"hep-th/9307065","kind":"arxiv","version":1}},"canonical_sha256":"6cb3b83a8cd23adfd89d0d5fdbcfa4aeae0f9fe36961087a7102536ac8010267","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cb3b83a8cd23adfd89d0d5fdbcfa4aeae0f9fe36961087a7102536ac8010267","first_computed_at":"2026-07-04T14:32:37.683997Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:32:37.683997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vIu6Axxo93vIMnv1Mmjbmht6E0Q2rDax2ZQ3jEzKdoSysqGyeIz29pLtpS6XKgL611jV8Amu/YskjP2MOFQzDQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:32:37.684400Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9307065","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04a677ef391b0d2074a416c8c5dda43fc8cf1a522b7709e7b9266bef0e2b45f5","sha256:368a6ba5e54466bd5e527313a0ceccdc17d2968088ffb428869fbc837121f19b"],"state_sha256":"0339b91e439a8f90cce637adc12b38ee1a12c10f153d535ae726dea899f2e4f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nMbgvAHtCbPqw++xrGddkR+3wTrSaE6ikUWmbF6PxV7gGn0ZX6yKCM162eXx5+9mYV0SMNS92QZ2RjNREsddAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T18:44:58.141277Z","bundle_sha256":"6cffcc6a0e1685ff567e9c7493cf234a2715fb834c0a76114030eac6836d8481"}}