{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:AVFJ6WJ25YUYZH7NB72LUQKCLO","short_pith_number":"pith:AVFJ6WJ2","canonical_record":{"source":{"id":"gr-qc/0109059","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2001-09-18T09:39:16Z","cross_cats_sorted":[],"title_canon_sha256":"7e480bd1205f8ee4f363aeb0f364c9da615f79da5f4a9cbdbfffaa706be052dc","abstract_canon_sha256":"e55e4fbe2c2c41af83b77283c2ef180f5ca880480a5ab8d093b387c917c6f54e"},"schema_version":"1.0"},"canonical_sha256":"054a9f593aee298c9fed0ff4ba41425bbdb3224a1327b3de5be40e97e6a74bdb","source":{"kind":"arxiv","id":"gr-qc/0109059","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0109059","created_at":"2026-05-18T04:17:53Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0109059v1","created_at":"2026-05-18T04:17:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0109059","created_at":"2026-05-18T04:17:53Z"},{"alias_kind":"pith_short_12","alias_value":"AVFJ6WJ25YUY","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"AVFJ6WJ25YUYZH7N","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"AVFJ6WJ2","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:AVFJ6WJ25YUYZH7NB72LUQKCLO","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/0109059","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2001-09-18T09:39:16Z","cross_cats_sorted":[],"title_canon_sha256":"7e480bd1205f8ee4f363aeb0f364c9da615f79da5f4a9cbdbfffaa706be052dc","abstract_canon_sha256":"e55e4fbe2c2c41af83b77283c2ef180f5ca880480a5ab8d093b387c917c6f54e"},"schema_version":"1.0"},"canonical_sha256":"054a9f593aee298c9fed0ff4ba41425bbdb3224a1327b3de5be40e97e6a74bdb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:17:53.117812Z","signature_b64":"bewARVWWES8UsA9BWFz8BlOObmYCI+50pklYGhDbX+DPH/QGB0SepI5f5andwZt/ptNMU0ygabJX4bFRYG6KAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"054a9f593aee298c9fed0ff4ba41425bbdb3224a1327b3de5be40e97e6a74bdb","last_reissued_at":"2026-05-18T04:17:53.117287Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:17:53.117287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/0109059","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":"2026-05-18T04:17:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kcvnoPXjGcP5YEmOnmSzwVB+wqzh8/vySp+nDzJOHR/9q2q99SX3ZcwX8BMvn/pkDu9L8D0hl6sVOio32rUABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:11:13.580535Z"},"content_sha256":"e1d1e40652b7566ccfdf889a274bc3f0cae696018dbfa8f92eb2317d8af66c37","schema_version":"1.0","event_id":"sha256:e1d1e40652b7566ccfdf889a274bc3f0cae696018dbfa8f92eb2317d8af66c37"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:AVFJ6WJ25YUYZH7NB72LUQKCLO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lectures on Quantum Cosmology","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"T. Christodoulakis","submitted_at":"2001-09-18T09:39:16Z","abstract_excerpt":"The problems encountered in trying to quantize the various cosmological models, are brought forward by means of a concrete example. The Automorphism groups are revealed as the key element through which G.C.T.'s can be used for a general treatment of these problems. At the classical level, the time dependent automorphisms lead to significant simplifications of the line element for the generic spatially homogeneous geometry, without loss of generality. At the quantum level, the ''frozen'' automorphisms entail an important reduction of the configuration space --spanned by the 6 components of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0109059","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":"2026-05-18T04:17:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ksi9VhlO0FjzsIXHvPDwD/R6qhz9L9vCy9Rt6z/60E57gcyBNL07wGvYZ3IGJfUc97nPpyzCL4BbAfVoN5h9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:11:13.580874Z"},"content_sha256":"b6da66dd91fc963d700abed0b1a0dc1a34e763e5fb2f31c61230c22b0a757a32","schema_version":"1.0","event_id":"sha256:b6da66dd91fc963d700abed0b1a0dc1a34e763e5fb2f31c61230c22b0a757a32"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AVFJ6WJ25YUYZH7NB72LUQKCLO/bundle.json","state_url":"https://pith.science/pith/AVFJ6WJ25YUYZH7NB72LUQKCLO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AVFJ6WJ25YUYZH7NB72LUQKCLO/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":"2026-05-28T11:11:13Z","links":{"resolver":"https://pith.science/pith/AVFJ6WJ25YUYZH7NB72LUQKCLO","bundle":"https://pith.science/pith/AVFJ6WJ25YUYZH7NB72LUQKCLO/bundle.json","state":"https://pith.science/pith/AVFJ6WJ25YUYZH7NB72LUQKCLO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AVFJ6WJ25YUYZH7NB72LUQKCLO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:AVFJ6WJ25YUYZH7NB72LUQKCLO","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":"e55e4fbe2c2c41af83b77283c2ef180f5ca880480a5ab8d093b387c917c6f54e","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2001-09-18T09:39:16Z","title_canon_sha256":"7e480bd1205f8ee4f363aeb0f364c9da615f79da5f4a9cbdbfffaa706be052dc"},"schema_version":"1.0","source":{"id":"gr-qc/0109059","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0109059","created_at":"2026-05-18T04:17:53Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0109059v1","created_at":"2026-05-18T04:17:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0109059","created_at":"2026-05-18T04:17:53Z"},{"alias_kind":"pith_short_12","alias_value":"AVFJ6WJ25YUY","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"AVFJ6WJ25YUYZH7N","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"AVFJ6WJ2","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:b6da66dd91fc963d700abed0b1a0dc1a34e763e5fb2f31c61230c22b0a757a32","target":"graph","created_at":"2026-05-18T04:17:53Z","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 problems encountered in trying to quantize the various cosmological models, are brought forward by means of a concrete example. The Automorphism groups are revealed as the key element through which G.C.T.'s can be used for a general treatment of these problems. At the classical level, the time dependent automorphisms lead to significant simplifications of the line element for the generic spatially homogeneous geometry, without loss of generality. At the quantum level, the ''frozen'' automorphisms entail an important reduction of the configuration space --spanned by the 6 components of the ","authors_text":"T. Christodoulakis","cross_cats":[],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2001-09-18T09:39:16Z","title":"Lectures on Quantum Cosmology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0109059","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:e1d1e40652b7566ccfdf889a274bc3f0cae696018dbfa8f92eb2317d8af66c37","target":"record","created_at":"2026-05-18T04:17:53Z","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":"e55e4fbe2c2c41af83b77283c2ef180f5ca880480a5ab8d093b387c917c6f54e","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2001-09-18T09:39:16Z","title_canon_sha256":"7e480bd1205f8ee4f363aeb0f364c9da615f79da5f4a9cbdbfffaa706be052dc"},"schema_version":"1.0","source":{"id":"gr-qc/0109059","kind":"arxiv","version":1}},"canonical_sha256":"054a9f593aee298c9fed0ff4ba41425bbdb3224a1327b3de5be40e97e6a74bdb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"054a9f593aee298c9fed0ff4ba41425bbdb3224a1327b3de5be40e97e6a74bdb","first_computed_at":"2026-05-18T04:17:53.117287Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:53.117287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bewARVWWES8UsA9BWFz8BlOObmYCI+50pklYGhDbX+DPH/QGB0SepI5f5andwZt/ptNMU0ygabJX4bFRYG6KAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:53.117812Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0109059","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1d1e40652b7566ccfdf889a274bc3f0cae696018dbfa8f92eb2317d8af66c37","sha256:b6da66dd91fc963d700abed0b1a0dc1a34e763e5fb2f31c61230c22b0a757a32"],"state_sha256":"e5d77b1b41769df9b3958d4532eda6f25adfbe18c7c048b417e6655840642b44"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aaY22cvFVoAXDVC04mAiANdn6pFnNV4Mv33HTt1YXAOqH2K6lzC+xP9sbLH2kdKeBMsiieNyqTEG9Tb5jWxeDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T11:11:13.582818Z","bundle_sha256":"b5844fa8ba5bebe49e422e58adf1685b9efc1ab8bd82e82b3aca943a5123ddd8"}}