{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5M74KRJQI36SP65YDM63MGX6WJ","short_pith_number":"pith:5M74KRJQ","canonical_record":{"source":{"id":"1509.03098","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-10T11:18:26Z","cross_cats_sorted":[],"title_canon_sha256":"8725f836170e9480b4c864b45c737158b7d515b75c97fb6406c30beee303435f","abstract_canon_sha256":"f774f654ade8bde730be6ae208fd3852e5101184e6ac27fbc4f1a2997786472b"},"schema_version":"1.0"},"canonical_sha256":"eb3fc5453046fd27fbb81b3db61afeb27dd3e2e2b06ff4a7dc6e435c1b3eb9ce","source":{"kind":"arxiv","id":"1509.03098","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03098","created_at":"2026-05-18T01:12:55Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03098v2","created_at":"2026-05-18T01:12:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03098","created_at":"2026-05-18T01:12:55Z"},{"alias_kind":"pith_short_12","alias_value":"5M74KRJQI36S","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5M74KRJQI36SP65Y","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5M74KRJQ","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5M74KRJQI36SP65YDM63MGX6WJ","target":"record","payload":{"canonical_record":{"source":{"id":"1509.03098","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-10T11:18:26Z","cross_cats_sorted":[],"title_canon_sha256":"8725f836170e9480b4c864b45c737158b7d515b75c97fb6406c30beee303435f","abstract_canon_sha256":"f774f654ade8bde730be6ae208fd3852e5101184e6ac27fbc4f1a2997786472b"},"schema_version":"1.0"},"canonical_sha256":"eb3fc5453046fd27fbb81b3db61afeb27dd3e2e2b06ff4a7dc6e435c1b3eb9ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:55.319887Z","signature_b64":"7kD+ZWiaGsxKYQuJoH7WXS0Za0IVUQVr5hqBpvMudo/ma9Aaj6gJ2kdq+2A38HEuhSNKCyOAy+pvXoq1oTbYBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb3fc5453046fd27fbb81b3db61afeb27dd3e2e2b06ff4a7dc6e435c1b3eb9ce","last_reissued_at":"2026-05-18T01:12:55.319471Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:55.319471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.03098","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":"2026-05-18T01:12:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"98D8M4Hl1R+qSCOcjohgu00TzNuyOFz4i3dKiIrI64fHjDsxbskTH2LnHZ0d+t18ofWwYlVmBESP9jalVGEDCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:59:50.138089Z"},"content_sha256":"7aca0a6764e4a9766fda34bb41b39ab925a35ede78355224e7da43b9b586a977","schema_version":"1.0","event_id":"sha256:7aca0a6764e4a9766fda34bb41b39ab925a35ede78355224e7da43b9b586a977"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5M74KRJQI36SP65YDM63MGX6WJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The extremal process of critical points of the pure $p$-spin spherical spin glass model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eliran Subag, Ofer Zeitouni","submitted_at":"2015-09-10T11:18:26Z","abstract_excerpt":"Recently, sharp results concerning the critical points of the Hamiltonian of the $p$-spin spherical spin glass model have been obtained by means of moments computations. In particular, these moments computations allow for the evaluation of the leading term of the ground-state, i.e., of the global minimum. In this paper, we study the extremal point process of critical points - that is, the point process associated to all critical values in the vicinity of the ground-state. We show that the latter converges in distribution to a Poisson point process of exponential intensity. In particular, we id"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03098","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":"2026-05-18T01:12:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M7XQNeHS10jQUntJIeyIzsY5m5qBQocrRkONKfJ3kXoSXCP3NQEXxPThRblXpA5weus9R33D29GyPYfd9ONWBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:59:50.138450Z"},"content_sha256":"867984ab426b82923ea510e01606a4f61ceea36146a4120e24f6a6ddffa36937","schema_version":"1.0","event_id":"sha256:867984ab426b82923ea510e01606a4f61ceea36146a4120e24f6a6ddffa36937"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5M74KRJQI36SP65YDM63MGX6WJ/bundle.json","state_url":"https://pith.science/pith/5M74KRJQI36SP65YDM63MGX6WJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5M74KRJQI36SP65YDM63MGX6WJ/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":"2026-06-03T08:59:50Z","links":{"resolver":"https://pith.science/pith/5M74KRJQI36SP65YDM63MGX6WJ","bundle":"https://pith.science/pith/5M74KRJQI36SP65YDM63MGX6WJ/bundle.json","state":"https://pith.science/pith/5M74KRJQI36SP65YDM63MGX6WJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5M74KRJQI36SP65YDM63MGX6WJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5M74KRJQI36SP65YDM63MGX6WJ","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":"f774f654ade8bde730be6ae208fd3852e5101184e6ac27fbc4f1a2997786472b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-10T11:18:26Z","title_canon_sha256":"8725f836170e9480b4c864b45c737158b7d515b75c97fb6406c30beee303435f"},"schema_version":"1.0","source":{"id":"1509.03098","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03098","created_at":"2026-05-18T01:12:55Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03098v2","created_at":"2026-05-18T01:12:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03098","created_at":"2026-05-18T01:12:55Z"},{"alias_kind":"pith_short_12","alias_value":"5M74KRJQI36S","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5M74KRJQI36SP65Y","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5M74KRJQ","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:867984ab426b82923ea510e01606a4f61ceea36146a4120e24f6a6ddffa36937","target":"graph","created_at":"2026-05-18T01:12:55Z","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":"Recently, sharp results concerning the critical points of the Hamiltonian of the $p$-spin spherical spin glass model have been obtained by means of moments computations. In particular, these moments computations allow for the evaluation of the leading term of the ground-state, i.e., of the global minimum. In this paper, we study the extremal point process of critical points - that is, the point process associated to all critical values in the vicinity of the ground-state. We show that the latter converges in distribution to a Poisson point process of exponential intensity. In particular, we id","authors_text":"Eliran Subag, Ofer Zeitouni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-10T11:18:26Z","title":"The extremal process of critical points of the pure $p$-spin spherical spin glass model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03098","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":"sha256:7aca0a6764e4a9766fda34bb41b39ab925a35ede78355224e7da43b9b586a977","target":"record","created_at":"2026-05-18T01:12:55Z","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":"f774f654ade8bde730be6ae208fd3852e5101184e6ac27fbc4f1a2997786472b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-10T11:18:26Z","title_canon_sha256":"8725f836170e9480b4c864b45c737158b7d515b75c97fb6406c30beee303435f"},"schema_version":"1.0","source":{"id":"1509.03098","kind":"arxiv","version":2}},"canonical_sha256":"eb3fc5453046fd27fbb81b3db61afeb27dd3e2e2b06ff4a7dc6e435c1b3eb9ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb3fc5453046fd27fbb81b3db61afeb27dd3e2e2b06ff4a7dc6e435c1b3eb9ce","first_computed_at":"2026-05-18T01:12:55.319471Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:55.319471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7kD+ZWiaGsxKYQuJoH7WXS0Za0IVUQVr5hqBpvMudo/ma9Aaj6gJ2kdq+2A38HEuhSNKCyOAy+pvXoq1oTbYBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:55.319887Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.03098","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7aca0a6764e4a9766fda34bb41b39ab925a35ede78355224e7da43b9b586a977","sha256:867984ab426b82923ea510e01606a4f61ceea36146a4120e24f6a6ddffa36937"],"state_sha256":"3c74a74defcac217f6cda49a0bbabc63f273ebee1f5264f72e99cb2b64058bcc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tUzSCno+mZ3q4QeV4gFJc6pk9LJTIYca1TxtbWbpNMFuaMqpZeDwcFGIhf06lhDgWgWP37/A0pl6jckUGKFABQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T08:59:50.140448Z","bundle_sha256":"83c1da33370eb2579027100d65e6fe526fc573536d083a84674bd32a04183f36"}}