{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:HPGBDKSQ6NYX4IUD2T3LDYME36","short_pith_number":"pith:HPGBDKSQ","canonical_record":{"source":{"id":"1205.3791","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-05-16T20:00:57Z","cross_cats_sorted":["gr-qc","hep-lat"],"title_canon_sha256":"4f33c254f3571a5a281edd03bac693aa9f6834199b15978d9b2693fdc62871fc","abstract_canon_sha256":"3872b3da4b4f8730c8d60697b5dde31b88b834311929a88eabd4b0f9dc0d94f6"},"schema_version":"1.0"},"canonical_sha256":"3bcc11aa50f3717e2283d4f6b1e184dfbaa09f72cae0ee52b588c40c5d48b1a1","source":{"kind":"arxiv","id":"1205.3791","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3791","created_at":"2026-05-18T01:21:08Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3791v1","created_at":"2026-05-18T01:21:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3791","created_at":"2026-05-18T01:21:08Z"},{"alias_kind":"pith_short_12","alias_value":"HPGBDKSQ6NYX","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HPGBDKSQ6NYX4IUD","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HPGBDKSQ","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:HPGBDKSQ6NYX4IUD2T3LDYME36","target":"record","payload":{"canonical_record":{"source":{"id":"1205.3791","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-05-16T20:00:57Z","cross_cats_sorted":["gr-qc","hep-lat"],"title_canon_sha256":"4f33c254f3571a5a281edd03bac693aa9f6834199b15978d9b2693fdc62871fc","abstract_canon_sha256":"3872b3da4b4f8730c8d60697b5dde31b88b834311929a88eabd4b0f9dc0d94f6"},"schema_version":"1.0"},"canonical_sha256":"3bcc11aa50f3717e2283d4f6b1e184dfbaa09f72cae0ee52b588c40c5d48b1a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:08.944844Z","signature_b64":"DmEIALykna++PJyy/2jgdAJwEu8Kku/3TxXS0rJMU6E47NhiucWQCsfbzoqsUAkxPHss46eYlxKTyer+mtREBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3bcc11aa50f3717e2283d4f6b1e184dfbaa09f72cae0ee52b588c40c5d48b1a1","last_reissued_at":"2026-05-18T01:21:08.944127Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:08.944127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.3791","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":"2026-05-18T01:21:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qd2EHPPNPg+/NquQ6G6J4vHQrpEarsqIiI3m0mBcTFQK6buJ2td72/GmYB916UIgTcb/l9AUtmK2miYd9kE6Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T13:15:41.667231Z"},"content_sha256":"fa4cefcba2fe3bebcff3ef231dd67e118b20d4dd0b0c9e2f500e1e0f89302361","schema_version":"1.0","event_id":"sha256:fa4cefcba2fe3bebcff3ef231dd67e118b20d4dd0b0c9e2f500e1e0f89302361"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:HPGBDKSQ6NYX4IUD2T3LDYME36","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The transfer matrix in four-dimensional CDT","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-lat"],"primary_cat":"hep-th","authors_text":"Andrzej G\\\"orlich, Jakub Gizbert-Studnicki, Jan Ambjorn, Jerzy Jurkiewicz","submitted_at":"2012-05-16T20:00:57Z","abstract_excerpt":"The Causal Dynamical Triangulation model of quantum gravity (CDT) has a transfer matrix, relating spatial geometries at adjacent (discrete lattice) times. The transfer matrix uniquely determines the theory. We show that the measurements of the scale factor of the (CDT) universe are well described by an effective transfer matrix where the matrix elements are labeled only by the scale factor. Using computer simulations we determine the effective transfer matrix elements and show how they relate to an effective minisuperspace action at all scales."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3791","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":""},"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":"2026-05-18T01:21:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MDjstxrRlRzOCWlKDrFqcVdXsXROCt8kaMD/Vm4i8VnvIMzqa0GUsLFp35uq5sMagiaveLyfBi5WpNGgJoo9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T13:15:41.668012Z"},"content_sha256":"065f1824457ec4ee30a5b53bcce47be3b7675f8a15d0777e9b3ace731eec2872","schema_version":"1.0","event_id":"sha256:065f1824457ec4ee30a5b53bcce47be3b7675f8a15d0777e9b3ace731eec2872"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HPGBDKSQ6NYX4IUD2T3LDYME36/bundle.json","state_url":"https://pith.science/pith/HPGBDKSQ6NYX4IUD2T3LDYME36/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HPGBDKSQ6NYX4IUD2T3LDYME36/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":"2026-06-10T13:15:41Z","links":{"resolver":"https://pith.science/pith/HPGBDKSQ6NYX4IUD2T3LDYME36","bundle":"https://pith.science/pith/HPGBDKSQ6NYX4IUD2T3LDYME36/bundle.json","state":"https://pith.science/pith/HPGBDKSQ6NYX4IUD2T3LDYME36/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HPGBDKSQ6NYX4IUD2T3LDYME36/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HPGBDKSQ6NYX4IUD2T3LDYME36","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":"3872b3da4b4f8730c8d60697b5dde31b88b834311929a88eabd4b0f9dc0d94f6","cross_cats_sorted":["gr-qc","hep-lat"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-05-16T20:00:57Z","title_canon_sha256":"4f33c254f3571a5a281edd03bac693aa9f6834199b15978d9b2693fdc62871fc"},"schema_version":"1.0","source":{"id":"1205.3791","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3791","created_at":"2026-05-18T01:21:08Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3791v1","created_at":"2026-05-18T01:21:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3791","created_at":"2026-05-18T01:21:08Z"},{"alias_kind":"pith_short_12","alias_value":"HPGBDKSQ6NYX","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HPGBDKSQ6NYX4IUD","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HPGBDKSQ","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:065f1824457ec4ee30a5b53bcce47be3b7675f8a15d0777e9b3ace731eec2872","target":"graph","created_at":"2026-05-18T01:21:08Z","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"},"paper":{"abstract_excerpt":"The Causal Dynamical Triangulation model of quantum gravity (CDT) has a transfer matrix, relating spatial geometries at adjacent (discrete lattice) times. The transfer matrix uniquely determines the theory. We show that the measurements of the scale factor of the (CDT) universe are well described by an effective transfer matrix where the matrix elements are labeled only by the scale factor. Using computer simulations we determine the effective transfer matrix elements and show how they relate to an effective minisuperspace action at all scales.","authors_text":"Andrzej G\\\"orlich, Jakub Gizbert-Studnicki, Jan Ambjorn, Jerzy Jurkiewicz","cross_cats":["gr-qc","hep-lat"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-05-16T20:00:57Z","title":"The transfer matrix in four-dimensional CDT"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3791","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:fa4cefcba2fe3bebcff3ef231dd67e118b20d4dd0b0c9e2f500e1e0f89302361","target":"record","created_at":"2026-05-18T01:21:08Z","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":"3872b3da4b4f8730c8d60697b5dde31b88b834311929a88eabd4b0f9dc0d94f6","cross_cats_sorted":["gr-qc","hep-lat"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-05-16T20:00:57Z","title_canon_sha256":"4f33c254f3571a5a281edd03bac693aa9f6834199b15978d9b2693fdc62871fc"},"schema_version":"1.0","source":{"id":"1205.3791","kind":"arxiv","version":1}},"canonical_sha256":"3bcc11aa50f3717e2283d4f6b1e184dfbaa09f72cae0ee52b588c40c5d48b1a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bcc11aa50f3717e2283d4f6b1e184dfbaa09f72cae0ee52b588c40c5d48b1a1","first_computed_at":"2026-05-18T01:21:08.944127Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:08.944127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DmEIALykna++PJyy/2jgdAJwEu8Kku/3TxXS0rJMU6E47NhiucWQCsfbzoqsUAkxPHss46eYlxKTyer+mtREBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:08.944844Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.3791","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa4cefcba2fe3bebcff3ef231dd67e118b20d4dd0b0c9e2f500e1e0f89302361","sha256:065f1824457ec4ee30a5b53bcce47be3b7675f8a15d0777e9b3ace731eec2872"],"state_sha256":"1af1ef0b767ed508843f0692d6eaa2d6d9fc5dec172057a9730a16fbbc3805a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zeR4J3Y3ZOEB1cIJzZz/3bLJ6PTFkaZMnZJ1Q0/HRLN7jy1BwOyHzOywBfSpBlS9hsYyxRUU15V+b2A6gO9hCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T13:15:41.671765Z","bundle_sha256":"bdaed1fea0afc35ee7e545e641f3588f800967096b2cbc2b4afd19b994cf9d0b"}}