{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:GWTNUHAGCYVRRRDVIJTY4ZYO4X","short_pith_number":"pith:GWTNUHAG","canonical_record":{"source":{"id":"2211.08920","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2022-11-16T14:05:23Z","cross_cats_sorted":["cond-mat.dis-nn","math.MP"],"title_canon_sha256":"8baccb8b626d0f5a26ef7094cbfa633f349149b81fb757f9f48a3ad93219b3c3","abstract_canon_sha256":"8c61a7baa59d32358f8058096e1ef56bfd28b196aefd601666c6e8cc8c15c7ea"},"schema_version":"1.0"},"canonical_sha256":"35a6da1c06162b18c47542678e670ee5ca7f7ba163bd823b3ea2436531c24955","source":{"kind":"arxiv","id":"2211.08920","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.08920","created_at":"2026-07-05T06:11:02Z"},{"alias_kind":"arxiv_version","alias_value":"2211.08920v2","created_at":"2026-07-05T06:11:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.08920","created_at":"2026-07-05T06:11:02Z"},{"alias_kind":"pith_short_12","alias_value":"GWTNUHAGCYVR","created_at":"2026-07-05T06:11:02Z"},{"alias_kind":"pith_short_16","alias_value":"GWTNUHAGCYVRRRDV","created_at":"2026-07-05T06:11:02Z"},{"alias_kind":"pith_short_8","alias_value":"GWTNUHAG","created_at":"2026-07-05T06:11:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:GWTNUHAGCYVRRRDVIJTY4ZYO4X","target":"record","payload":{"canonical_record":{"source":{"id":"2211.08920","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2022-11-16T14:05:23Z","cross_cats_sorted":["cond-mat.dis-nn","math.MP"],"title_canon_sha256":"8baccb8b626d0f5a26ef7094cbfa633f349149b81fb757f9f48a3ad93219b3c3","abstract_canon_sha256":"8c61a7baa59d32358f8058096e1ef56bfd28b196aefd601666c6e8cc8c15c7ea"},"schema_version":"1.0"},"canonical_sha256":"35a6da1c06162b18c47542678e670ee5ca7f7ba163bd823b3ea2436531c24955","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:11:02.081518Z","signature_b64":"l1KuS4GB2U1GomgZ8pXUAo5N1+vs30Kg9hWxPK9GyePkQ82cEM2o7Q4NnTlF0C0PmNwM+mqqbcWeDQkdmtmDCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35a6da1c06162b18c47542678e670ee5ca7f7ba163bd823b3ea2436531c24955","last_reissued_at":"2026-07-05T06:11:02.081096Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:11:02.081096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.08920","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:11:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zslmNz+ghTntfp6Ew+BuqqerhT0B+nQIs2qCO7NHjni+xwTiE9Tr4EViv3YpNoUkJUjhvTDdBclI3ece08haDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T08:09:10.491660Z"},"content_sha256":"b6e23581331f806505347f1b6439f35f3b06650749f0c5bc7cd1715c824fe586","schema_version":"1.0","event_id":"sha256:b6e23581331f806505347f1b6439f35f3b06650749f0c5bc7cd1715c824fe586"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:GWTNUHAGCYVRRRDVIJTY4ZYO4X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinite volume Gibbs states and metastates of the random field mean-field spherical model","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.MP"],"primary_cat":"math-ph","authors_text":"Kalle Koskinen","submitted_at":"2022-11-16T14:05:23Z","abstract_excerpt":"For the discrete random field Curie-Weiss models, the infinite volume Gibbs states and metastates have been investigated and determined for specific instances of random external fields. In general, there are not many examples in the literature of non-trivial limiting metastates for discrete or continuous spin systems. We analyze the infinite volume Gibbs states of the mean-field spherical model, a model of continuous spins, in a general random external field with independent identically distributed components with finite moments of some order larger than four and non-vanishing variances of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.08920","kind":"arxiv","version":2},"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/2211.08920/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":"2026-07-05T06:11:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QBW0VL7Tf/6qUw+kZ/gKCQZtOkfr+/cmz6Wea/NCFP8HTZKM3XFulZBdPzgEBdukbzmO1SPjQsmxcH0+DiZKBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T08:09:10.492250Z"},"content_sha256":"27799b63f106ed12b9812fb8ace43bfe3e2488e11f483bd07b057aafd15af978","schema_version":"1.0","event_id":"sha256:27799b63f106ed12b9812fb8ace43bfe3e2488e11f483bd07b057aafd15af978"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GWTNUHAGCYVRRRDVIJTY4ZYO4X/bundle.json","state_url":"https://pith.science/pith/GWTNUHAGCYVRRRDVIJTY4ZYO4X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GWTNUHAGCYVRRRDVIJTY4ZYO4X/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":"2026-08-07T08:09:10Z","links":{"resolver":"https://pith.science/pith/GWTNUHAGCYVRRRDVIJTY4ZYO4X","bundle":"https://pith.science/pith/GWTNUHAGCYVRRRDVIJTY4ZYO4X/bundle.json","state":"https://pith.science/pith/GWTNUHAGCYVRRRDVIJTY4ZYO4X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GWTNUHAGCYVRRRDVIJTY4ZYO4X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:GWTNUHAGCYVRRRDVIJTY4ZYO4X","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":"8c61a7baa59d32358f8058096e1ef56bfd28b196aefd601666c6e8cc8c15c7ea","cross_cats_sorted":["cond-mat.dis-nn","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2022-11-16T14:05:23Z","title_canon_sha256":"8baccb8b626d0f5a26ef7094cbfa633f349149b81fb757f9f48a3ad93219b3c3"},"schema_version":"1.0","source":{"id":"2211.08920","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.08920","created_at":"2026-07-05T06:11:02Z"},{"alias_kind":"arxiv_version","alias_value":"2211.08920v2","created_at":"2026-07-05T06:11:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.08920","created_at":"2026-07-05T06:11:02Z"},{"alias_kind":"pith_short_12","alias_value":"GWTNUHAGCYVR","created_at":"2026-07-05T06:11:02Z"},{"alias_kind":"pith_short_16","alias_value":"GWTNUHAGCYVRRRDV","created_at":"2026-07-05T06:11:02Z"},{"alias_kind":"pith_short_8","alias_value":"GWTNUHAG","created_at":"2026-07-05T06:11:02Z"}],"graph_snapshots":[{"event_id":"sha256:27799b63f106ed12b9812fb8ace43bfe3e2488e11f483bd07b057aafd15af978","target":"graph","created_at":"2026-07-05T06:11:02Z","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/2211.08920/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For the discrete random field Curie-Weiss models, the infinite volume Gibbs states and metastates have been investigated and determined for specific instances of random external fields. In general, there are not many examples in the literature of non-trivial limiting metastates for discrete or continuous spin systems. We analyze the infinite volume Gibbs states of the mean-field spherical model, a model of continuous spins, in a general random external field with independent identically distributed components with finite moments of some order larger than four and non-vanishing variances of the","authors_text":"Kalle Koskinen","cross_cats":["cond-mat.dis-nn","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2022-11-16T14:05:23Z","title":"Infinite volume Gibbs states and metastates of the random field mean-field spherical model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.08920","kind":"arxiv","version":2},"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:b6e23581331f806505347f1b6439f35f3b06650749f0c5bc7cd1715c824fe586","target":"record","created_at":"2026-07-05T06:11:02Z","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":"8c61a7baa59d32358f8058096e1ef56bfd28b196aefd601666c6e8cc8c15c7ea","cross_cats_sorted":["cond-mat.dis-nn","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2022-11-16T14:05:23Z","title_canon_sha256":"8baccb8b626d0f5a26ef7094cbfa633f349149b81fb757f9f48a3ad93219b3c3"},"schema_version":"1.0","source":{"id":"2211.08920","kind":"arxiv","version":2}},"canonical_sha256":"35a6da1c06162b18c47542678e670ee5ca7f7ba163bd823b3ea2436531c24955","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35a6da1c06162b18c47542678e670ee5ca7f7ba163bd823b3ea2436531c24955","first_computed_at":"2026-07-05T06:11:02.081096Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:11:02.081096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l1KuS4GB2U1GomgZ8pXUAo5N1+vs30Kg9hWxPK9GyePkQ82cEM2o7Q4NnTlF0C0PmNwM+mqqbcWeDQkdmtmDCA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:11:02.081518Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.08920","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6e23581331f806505347f1b6439f35f3b06650749f0c5bc7cd1715c824fe586","sha256:27799b63f106ed12b9812fb8ace43bfe3e2488e11f483bd07b057aafd15af978"],"state_sha256":"310f403ce6d4c76a8956764ea0821a3a6864286015671a23326bfcd3ebd14f26"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FcS7ApHRCQqWB6BgZ4Ae7fOCwRSgVJIlK4ytqizKV0bPEJKbZybqhasEAi0kZVLsJumvfwjwTcedtTfcA3wwCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T08:09:10.498957Z","bundle_sha256":"3c982168bf0438d628a3815bcb68a3893c8e798c00f1b5c997f99e763a176683"}}