{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:5V4VZ5CW3OR5A2HDEB37NWIEGS","short_pith_number":"pith:5V4VZ5CW","canonical_record":{"source":{"id":"math/0609353","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2006-09-13T12:44:39Z","cross_cats_sorted":[],"title_canon_sha256":"50a394bf315df8a1375d34d01a248ebe0b112aaa41d80b90ac4dcb59157aabb7","abstract_canon_sha256":"bfeed4e12eb2a17846613cc75a955e71863f7886b3fbdf4b02c66bcad2bd0d4f"},"schema_version":"1.0"},"canonical_sha256":"ed795cf456dba3d068e32077f6d9043490e27b9ca58fe7ef28547c94cea577d9","source":{"kind":"arxiv","id":"math/0609353","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0609353","created_at":"2026-05-18T01:08:49Z"},{"alias_kind":"arxiv_version","alias_value":"math/0609353v1","created_at":"2026-05-18T01:08:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0609353","created_at":"2026-05-18T01:08:49Z"},{"alias_kind":"pith_short_12","alias_value":"5V4VZ5CW3OR5","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"5V4VZ5CW3OR5A2HD","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"5V4VZ5CW","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:5V4VZ5CW3OR5A2HDEB37NWIEGS","target":"record","payload":{"canonical_record":{"source":{"id":"math/0609353","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2006-09-13T12:44:39Z","cross_cats_sorted":[],"title_canon_sha256":"50a394bf315df8a1375d34d01a248ebe0b112aaa41d80b90ac4dcb59157aabb7","abstract_canon_sha256":"bfeed4e12eb2a17846613cc75a955e71863f7886b3fbdf4b02c66bcad2bd0d4f"},"schema_version":"1.0"},"canonical_sha256":"ed795cf456dba3d068e32077f6d9043490e27b9ca58fe7ef28547c94cea577d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:49.737860Z","signature_b64":"WKhO4Xa8mvMzF6hRwZ7QJpS3bqBtr9x3u+wOE/fKE5t66VKZax8+uHY2IrVzqxYDmPOiWp4XCyBWNYuwq7LWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed795cf456dba3d068e32077f6d9043490e27b9ca58fe7ef28547c94cea577d9","last_reissued_at":"2026-05-18T01:08:49.736993Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:49.736993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0609353","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":"2026-05-18T01:08:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TX4ou3A8U8nX09dlv8E6D8lPsaWJmFXW8+byXYgluVHao/TXYACoaVBI6mo4JkWGe0dnGHjb6zdItKxlKpU3DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T17:55:24.146912Z"},"content_sha256":"e8af548366a7feee261e9398871dc75edaecdf2cd05b3979227a1b56ab7b0d20","schema_version":"1.0","event_id":"sha256:e8af548366a7feee261e9398871dc75edaecdf2cd05b3979227a1b56ab7b0d20"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:5V4VZ5CW3OR5A2HDEB37NWIEGS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast simulated annealing in $\\R^d$ and an application to maximum likelihood estimation","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Magnus Wiktorsson (CENTRE for Mathematical Sciences), Sylvain Rubenthaler (JAD), Tobias Ryd\\'en (CENTRE for Mathematical Sciences)","submitted_at":"2006-09-13T12:44:39Z","abstract_excerpt":"Using classical simulated annealing to maximise a function $\\psi$ defined on a subset of $\\R^d$, the probability $\\p(\\psi(\\theta\\_n)\\leq \\psi\\_{\\max}-\\epsilon)$ tends to zero at a logarithmic rate as $n$ increases; here $\\theta\\_n$ is the state in the $n$-th stage of the simulated annealing algorithm and $\\psi\\_{\\max}$ is the maximal value of $\\psi$. We propose a modified scheme for which this probability is of order $n^{-1/3}\\log n$, and hence vanishes at an algebraic rate. To obtain this faster rate, the exponentially decaying acceptance probability of classical simulated annealing is replac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609353","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":"2026-05-18T01:08:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XlS2QLxp0F+WKId6/1rMvmo0bn0my917ja2njWWiT6vCYYJV5VTwy0Rr7IrKdFd7mlJchKCDNjHp4thItsZrBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T17:55:24.147255Z"},"content_sha256":"d2eba0e03b1bef2c67b43edf724a4789621241f2a4b8155fe1f653ade809cf60","schema_version":"1.0","event_id":"sha256:d2eba0e03b1bef2c67b43edf724a4789621241f2a4b8155fe1f653ade809cf60"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5V4VZ5CW3OR5A2HDEB37NWIEGS/bundle.json","state_url":"https://pith.science/pith/5V4VZ5CW3OR5A2HDEB37NWIEGS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5V4VZ5CW3OR5A2HDEB37NWIEGS/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":"2026-06-30T17:55:24Z","links":{"resolver":"https://pith.science/pith/5V4VZ5CW3OR5A2HDEB37NWIEGS","bundle":"https://pith.science/pith/5V4VZ5CW3OR5A2HDEB37NWIEGS/bundle.json","state":"https://pith.science/pith/5V4VZ5CW3OR5A2HDEB37NWIEGS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5V4VZ5CW3OR5A2HDEB37NWIEGS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:5V4VZ5CW3OR5A2HDEB37NWIEGS","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":"bfeed4e12eb2a17846613cc75a955e71863f7886b3fbdf4b02c66bcad2bd0d4f","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2006-09-13T12:44:39Z","title_canon_sha256":"50a394bf315df8a1375d34d01a248ebe0b112aaa41d80b90ac4dcb59157aabb7"},"schema_version":"1.0","source":{"id":"math/0609353","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0609353","created_at":"2026-05-18T01:08:49Z"},{"alias_kind":"arxiv_version","alias_value":"math/0609353v1","created_at":"2026-05-18T01:08:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0609353","created_at":"2026-05-18T01:08:49Z"},{"alias_kind":"pith_short_12","alias_value":"5V4VZ5CW3OR5","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"5V4VZ5CW3OR5A2HD","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"5V4VZ5CW","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:d2eba0e03b1bef2c67b43edf724a4789621241f2a4b8155fe1f653ade809cf60","target":"graph","created_at":"2026-05-18T01:08:49Z","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":"Using classical simulated annealing to maximise a function $\\psi$ defined on a subset of $\\R^d$, the probability $\\p(\\psi(\\theta\\_n)\\leq \\psi\\_{\\max}-\\epsilon)$ tends to zero at a logarithmic rate as $n$ increases; here $\\theta\\_n$ is the state in the $n$-th stage of the simulated annealing algorithm and $\\psi\\_{\\max}$ is the maximal value of $\\psi$. We propose a modified scheme for which this probability is of order $n^{-1/3}\\log n$, and hence vanishes at an algebraic rate. To obtain this faster rate, the exponentially decaying acceptance probability of classical simulated annealing is replac","authors_text":"Magnus Wiktorsson (CENTRE for Mathematical Sciences), Sylvain Rubenthaler (JAD), Tobias Ryd\\'en (CENTRE for Mathematical Sciences)","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2006-09-13T12:44:39Z","title":"Fast simulated annealing in $\\R^d$ and an application to maximum likelihood estimation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609353","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:e8af548366a7feee261e9398871dc75edaecdf2cd05b3979227a1b56ab7b0d20","target":"record","created_at":"2026-05-18T01:08:49Z","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":"bfeed4e12eb2a17846613cc75a955e71863f7886b3fbdf4b02c66bcad2bd0d4f","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2006-09-13T12:44:39Z","title_canon_sha256":"50a394bf315df8a1375d34d01a248ebe0b112aaa41d80b90ac4dcb59157aabb7"},"schema_version":"1.0","source":{"id":"math/0609353","kind":"arxiv","version":1}},"canonical_sha256":"ed795cf456dba3d068e32077f6d9043490e27b9ca58fe7ef28547c94cea577d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed795cf456dba3d068e32077f6d9043490e27b9ca58fe7ef28547c94cea577d9","first_computed_at":"2026-05-18T01:08:49.736993Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:49.736993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WKhO4Xa8mvMzF6hRwZ7QJpS3bqBtr9x3u+wOE/fKE5t66VKZax8+uHY2IrVzqxYDmPOiWp4XCyBWNYuwq7LWAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:49.737860Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0609353","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8af548366a7feee261e9398871dc75edaecdf2cd05b3979227a1b56ab7b0d20","sha256:d2eba0e03b1bef2c67b43edf724a4789621241f2a4b8155fe1f653ade809cf60"],"state_sha256":"687a26b63d6dbde5973139a7d44b7ebb93fa7eed09ba715b99360985e474d8d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nMCbLShkKQA3QnL05fd+DxKEZZj/uhORXiOFb1UBqXhcOBHyM0cMERrFmidolCzamc/2cCbPqJkGXdLuZFVuBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T17:55:24.149184Z","bundle_sha256":"1694ae29e532c3db70c06140f792004a31a1e6653e83f9d474650bf3f071e786"}}