{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:F63DAN7LWVUFXM2CUJPFSQJYQP","short_pith_number":"pith:F63DAN7L","canonical_record":{"source":{"id":"1507.05067","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-17T18:36:59Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"16829005ea6388453d12ac018f5d5eb5f37291e3eb839c9e8db222fc398a989c","abstract_canon_sha256":"0a131fc330f33a85b8663eb20827b698e7affed66fabadb872c4e888b2398d45"},"schema_version":"1.0"},"canonical_sha256":"2fb63037ebb5685bb342a25e59413883f45237b297011200503ab879ea41e93b","source":{"kind":"arxiv","id":"1507.05067","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05067","created_at":"2026-05-18T01:21:55Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05067v2","created_at":"2026-05-18T01:21:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05067","created_at":"2026-05-18T01:21:55Z"},{"alias_kind":"pith_short_12","alias_value":"F63DAN7LWVUF","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"F63DAN7LWVUFXM2C","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"F63DAN7L","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:F63DAN7LWVUFXM2CUJPFSQJYQP","target":"record","payload":{"canonical_record":{"source":{"id":"1507.05067","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-17T18:36:59Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"16829005ea6388453d12ac018f5d5eb5f37291e3eb839c9e8db222fc398a989c","abstract_canon_sha256":"0a131fc330f33a85b8663eb20827b698e7affed66fabadb872c4e888b2398d45"},"schema_version":"1.0"},"canonical_sha256":"2fb63037ebb5685bb342a25e59413883f45237b297011200503ab879ea41e93b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:55.034852Z","signature_b64":"dQuBfIthNgLvAYI4Oc7RAhNMB5kaqF2sk4kBcWivjm0YgnEXiq5uhHBMjFJ41L8Ulsq7Tp1HrREpS05tncoBCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fb63037ebb5685bb342a25e59413883f45237b297011200503ab879ea41e93b","last_reissued_at":"2026-05-18T01:21:55.034098Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:55.034098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.05067","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":"2026-05-18T01:21:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kCGe1ER6XaclSB3ywFGkoHTrcUm7Gsqwo9uRcqudUHl30E7z1D5ogMyxNeKwpzfHs0qcqxhxlscIzgjke0UtDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:08:12.405933Z"},"content_sha256":"8b70d1b529a497847c96306b2bdb99c1b4e9441460df846ebddf18386cb3cd26","schema_version":"1.0","event_id":"sha256:8b70d1b529a497847c96306b2bdb99c1b4e9441460df846ebddf18386cb3cd26"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:F63DAN7LWVUFXM2CUJPFSQJYQP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"High Temperature Asymptotics of Orthogonal Mean-Field Spin Glasses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Bhaswar B. Bhattacharya, Subhabrata Sen","submitted_at":"2015-07-17T18:36:59Z","abstract_excerpt":"We evaluate the high temperature limit of the free energy of spin glasses on the hypercube with Hamiltonian $H_N(\\sigma) = \\sigma^T J \\sigma$, where the coupling matrix $J$ is drawn from certain symmetric orthogonally invariant ensembles. Our derivation relates the annealed free energy of these models to a spherical integral, and expresses the limit of the free energy in terms of the limiting spectral measure of the coupling matrix $J$. As an application, we derive the limiting free energy of the Random Orthogonal Model (ROM) at high temperatures, which confirms non-rigorous calculations of Ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05067","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":""},"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":"2026-05-18T01:21:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hRc/o6s1jWUbBJDbgr2Z3kUXvvkv2/2jfuXIMsrjTQOaHDI8yq33kEPZkkEha/b1qQJ1QG7lPG/KlS5MQSEzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:08:12.406690Z"},"content_sha256":"7bdfd10c44d3102640b67cb013e78672a56f42564da4ba936836a554f594291f","schema_version":"1.0","event_id":"sha256:7bdfd10c44d3102640b67cb013e78672a56f42564da4ba936836a554f594291f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F63DAN7LWVUFXM2CUJPFSQJYQP/bundle.json","state_url":"https://pith.science/pith/F63DAN7LWVUFXM2CUJPFSQJYQP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F63DAN7LWVUFXM2CUJPFSQJYQP/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":"2026-05-28T20:08:12Z","links":{"resolver":"https://pith.science/pith/F63DAN7LWVUFXM2CUJPFSQJYQP","bundle":"https://pith.science/pith/F63DAN7LWVUFXM2CUJPFSQJYQP/bundle.json","state":"https://pith.science/pith/F63DAN7LWVUFXM2CUJPFSQJYQP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F63DAN7LWVUFXM2CUJPFSQJYQP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:F63DAN7LWVUFXM2CUJPFSQJYQP","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":"0a131fc330f33a85b8663eb20827b698e7affed66fabadb872c4e888b2398d45","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-17T18:36:59Z","title_canon_sha256":"16829005ea6388453d12ac018f5d5eb5f37291e3eb839c9e8db222fc398a989c"},"schema_version":"1.0","source":{"id":"1507.05067","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05067","created_at":"2026-05-18T01:21:55Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05067v2","created_at":"2026-05-18T01:21:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05067","created_at":"2026-05-18T01:21:55Z"},{"alias_kind":"pith_short_12","alias_value":"F63DAN7LWVUF","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"F63DAN7LWVUFXM2C","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"F63DAN7L","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:7bdfd10c44d3102640b67cb013e78672a56f42564da4ba936836a554f594291f","target":"graph","created_at":"2026-05-18T01:21:55Z","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":"We evaluate the high temperature limit of the free energy of spin glasses on the hypercube with Hamiltonian $H_N(\\sigma) = \\sigma^T J \\sigma$, where the coupling matrix $J$ is drawn from certain symmetric orthogonally invariant ensembles. Our derivation relates the annealed free energy of these models to a spherical integral, and expresses the limit of the free energy in terms of the limiting spectral measure of the coupling matrix $J$. As an application, we derive the limiting free energy of the Random Orthogonal Model (ROM) at high temperatures, which confirms non-rigorous calculations of Ma","authors_text":"Bhaswar B. Bhattacharya, Subhabrata Sen","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-17T18:36:59Z","title":"High Temperature Asymptotics of Orthogonal Mean-Field Spin Glasses"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05067","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":"sha256:8b70d1b529a497847c96306b2bdb99c1b4e9441460df846ebddf18386cb3cd26","target":"record","created_at":"2026-05-18T01:21:55Z","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":"0a131fc330f33a85b8663eb20827b698e7affed66fabadb872c4e888b2398d45","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-17T18:36:59Z","title_canon_sha256":"16829005ea6388453d12ac018f5d5eb5f37291e3eb839c9e8db222fc398a989c"},"schema_version":"1.0","source":{"id":"1507.05067","kind":"arxiv","version":2}},"canonical_sha256":"2fb63037ebb5685bb342a25e59413883f45237b297011200503ab879ea41e93b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fb63037ebb5685bb342a25e59413883f45237b297011200503ab879ea41e93b","first_computed_at":"2026-05-18T01:21:55.034098Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:55.034098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dQuBfIthNgLvAYI4Oc7RAhNMB5kaqF2sk4kBcWivjm0YgnEXiq5uhHBMjFJ41L8Ulsq7Tp1HrREpS05tncoBCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:55.034852Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.05067","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b70d1b529a497847c96306b2bdb99c1b4e9441460df846ebddf18386cb3cd26","sha256:7bdfd10c44d3102640b67cb013e78672a56f42564da4ba936836a554f594291f"],"state_sha256":"edbf4429bde77a9ed7d6823953e823f7efe244b60db3e87a088d852124748766"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xv5DP5nOj0LqwjRS8p+5Qufd93hd5NPHs9423tMzUAgaWAxqpd2y3EbLqSXXYTuW1jyHtFo83m+m64uviP1CDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:08:12.410790Z","bundle_sha256":"523f63bb9cedad29d980ac6ffc886239ef7ea1211fa34c324e3bc9d366ea0770"}}