{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:IM7HWRR5EHAE5EB433TAXXB3NU","short_pith_number":"pith:IM7HWRR5","canonical_record":{"source":{"id":"gr-qc/0108068","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2001-08-28T10:32:09Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"df5699c6586be2fb7811bf6e2da0de6ee9e654cfdfc447b97a0e1566520efaab","abstract_canon_sha256":"31e322c0dbe6f10f2d4ee2ed44886619ec53ddcd1d82bc227bd31f222f08b388"},"schema_version":"1.0"},"canonical_sha256":"433e7b463d21c04e903cdee60bdc3b6d2aa39e0b04ea3b762bbc4a5dac400031","source":{"kind":"arxiv","id":"gr-qc/0108068","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0108068","created_at":"2026-05-18T01:39:24Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0108068v1","created_at":"2026-05-18T01:39:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0108068","created_at":"2026-05-18T01:39:24Z"},{"alias_kind":"pith_short_12","alias_value":"IM7HWRR5EHAE","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"IM7HWRR5EHAE5EB4","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"IM7HWRR5","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:IM7HWRR5EHAE5EB433TAXXB3NU","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/0108068","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2001-08-28T10:32:09Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"df5699c6586be2fb7811bf6e2da0de6ee9e654cfdfc447b97a0e1566520efaab","abstract_canon_sha256":"31e322c0dbe6f10f2d4ee2ed44886619ec53ddcd1d82bc227bd31f222f08b388"},"schema_version":"1.0"},"canonical_sha256":"433e7b463d21c04e903cdee60bdc3b6d2aa39e0b04ea3b762bbc4a5dac400031","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:24.135773Z","signature_b64":"ei4FgYIfSmHtavuDTg6xpVr+2OftCczKVjd0grmRSsC48qCqGM+XWR8bawDuv8huowo/GRT+bRBnySwVMMoHCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"433e7b463d21c04e903cdee60bdc3b6d2aa39e0b04ea3b762bbc4a5dac400031","last_reissued_at":"2026-05-18T01:39:24.135232Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:24.135232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/0108068","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":"2026-05-18T01:39:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oDCxMget0yfHQlwbGWi/JMp3Rm/B23eyuh7kklgq/69GfNDXQ82gYN5TPAf1bpTOKoWw/ITEgOn+/1wj+ceQDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:18:18.941844Z"},"content_sha256":"571cf967d8769da301a407579472c939394d66c3b28e359bd25b8b6a24828248","schema_version":"1.0","event_id":"sha256:571cf967d8769da301a407579472c939394d66c3b28e359bd25b8b6a24828248"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:IM7HWRR5EHAE5EB433TAXXB3NU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gibbs and Quantum Discrete Spaces","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"V. A. Malyshev","submitted_at":"2001-08-28T10:32:09Z","abstract_excerpt":"Gibbs measure is one of the central objects of the modern probability, mathematical statistical physics and euclidean quantum field theory. Here we define and study its natural generalization for the case when the space, where the random field is defined is itself random. Moreover, this randomness is not given apriori and independently of the configuration, but rather they depend on each other, and both are given by Gibbs procedure; We call the resulting object a Gibbs family because it parametrizes Gibbs fields on different graphs in the support of the distribution. We study also quantum (KMS"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0108068","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":"2026-05-18T01:39:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3t6eOEB0yq+/VXj1INzQEypMxky8jDoAdUx+cRBxoTCKaCssY35Z/NaXh5tHjc5uLuzr4THD7kMmAGcBqKAeCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:18:18.942189Z"},"content_sha256":"9a4d6e320152a622ff576f7f56f485656d51341826d9c22f8a5b8dbc6c89fecb","schema_version":"1.0","event_id":"sha256:9a4d6e320152a622ff576f7f56f485656d51341826d9c22f8a5b8dbc6c89fecb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IM7HWRR5EHAE5EB433TAXXB3NU/bundle.json","state_url":"https://pith.science/pith/IM7HWRR5EHAE5EB433TAXXB3NU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IM7HWRR5EHAE5EB433TAXXB3NU/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":"2026-06-20T07:18:18Z","links":{"resolver":"https://pith.science/pith/IM7HWRR5EHAE5EB433TAXXB3NU","bundle":"https://pith.science/pith/IM7HWRR5EHAE5EB433TAXXB3NU/bundle.json","state":"https://pith.science/pith/IM7HWRR5EHAE5EB433TAXXB3NU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IM7HWRR5EHAE5EB433TAXXB3NU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:IM7HWRR5EHAE5EB433TAXXB3NU","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":"31e322c0dbe6f10f2d4ee2ed44886619ec53ddcd1d82bc227bd31f222f08b388","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"gr-qc","submitted_at":"2001-08-28T10:32:09Z","title_canon_sha256":"df5699c6586be2fb7811bf6e2da0de6ee9e654cfdfc447b97a0e1566520efaab"},"schema_version":"1.0","source":{"id":"gr-qc/0108068","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0108068","created_at":"2026-05-18T01:39:24Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0108068v1","created_at":"2026-05-18T01:39:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0108068","created_at":"2026-05-18T01:39:24Z"},{"alias_kind":"pith_short_12","alias_value":"IM7HWRR5EHAE","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"IM7HWRR5EHAE5EB4","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"IM7HWRR5","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:9a4d6e320152a622ff576f7f56f485656d51341826d9c22f8a5b8dbc6c89fecb","target":"graph","created_at":"2026-05-18T01:39:24Z","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":"Gibbs measure is one of the central objects of the modern probability, mathematical statistical physics and euclidean quantum field theory. Here we define and study its natural generalization for the case when the space, where the random field is defined is itself random. Moreover, this randomness is not given apriori and independently of the configuration, but rather they depend on each other, and both are given by Gibbs procedure; We call the resulting object a Gibbs family because it parametrizes Gibbs fields on different graphs in the support of the distribution. We study also quantum (KMS","authors_text":"V. A. Malyshev","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2001-08-28T10:32:09Z","title":"Gibbs and Quantum Discrete Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0108068","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":"sha256:571cf967d8769da301a407579472c939394d66c3b28e359bd25b8b6a24828248","target":"record","created_at":"2026-05-18T01:39:24Z","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":"31e322c0dbe6f10f2d4ee2ed44886619ec53ddcd1d82bc227bd31f222f08b388","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"gr-qc","submitted_at":"2001-08-28T10:32:09Z","title_canon_sha256":"df5699c6586be2fb7811bf6e2da0de6ee9e654cfdfc447b97a0e1566520efaab"},"schema_version":"1.0","source":{"id":"gr-qc/0108068","kind":"arxiv","version":1}},"canonical_sha256":"433e7b463d21c04e903cdee60bdc3b6d2aa39e0b04ea3b762bbc4a5dac400031","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"433e7b463d21c04e903cdee60bdc3b6d2aa39e0b04ea3b762bbc4a5dac400031","first_computed_at":"2026-05-18T01:39:24.135232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:24.135232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ei4FgYIfSmHtavuDTg6xpVr+2OftCczKVjd0grmRSsC48qCqGM+XWR8bawDuv8huowo/GRT+bRBnySwVMMoHCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:24.135773Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0108068","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:571cf967d8769da301a407579472c939394d66c3b28e359bd25b8b6a24828248","sha256:9a4d6e320152a622ff576f7f56f485656d51341826d9c22f8a5b8dbc6c89fecb"],"state_sha256":"f45510b2d33a506b2cdf8acc15384c4ed5dfe997d0caad2ed7f396bf07694ed3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XWjKyb0pI6fHqwsOGPR5GBPEFroN+ZaLp/NXuyq0y9yNa3GC2utEDMikRoWsRcKImdYDaElcgp2AnNZME6U7Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T07:18:18.944132Z","bundle_sha256":"babe2e5b432c4ad730d5e4bba42d70380ebc91990796a54ec8f6157964629974"}}