{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JNF5YRYMXE6RYFW3V77XVIRNBK","short_pith_number":"pith:JNF5YRYM","canonical_record":{"source":{"id":"1510.00112","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-01T05:42:25Z","cross_cats_sorted":["math.IT","stat.ME","stat.ML"],"title_canon_sha256":"741221aec2c6222fa808776c90ca7c713c73daa03464ecee683d02501edac9be","abstract_canon_sha256":"56efe983b64db0593753c24196da27e340789667c8898c0818147b7a4b49bcd8"},"schema_version":"1.0"},"canonical_sha256":"4b4bdc470cb93d1c16dbafff7aa22d0aa18eafe808a42f51b43000f2bd803964","source":{"kind":"arxiv","id":"1510.00112","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.00112","created_at":"2026-05-18T01:28:33Z"},{"alias_kind":"arxiv_version","alias_value":"1510.00112v3","created_at":"2026-05-18T01:28:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00112","created_at":"2026-05-18T01:28:33Z"},{"alias_kind":"pith_short_12","alias_value":"JNF5YRYMXE6R","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JNF5YRYMXE6RYFW3","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JNF5YRYM","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JNF5YRYMXE6RYFW3V77XVIRNBK","target":"record","payload":{"canonical_record":{"source":{"id":"1510.00112","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-01T05:42:25Z","cross_cats_sorted":["math.IT","stat.ME","stat.ML"],"title_canon_sha256":"741221aec2c6222fa808776c90ca7c713c73daa03464ecee683d02501edac9be","abstract_canon_sha256":"56efe983b64db0593753c24196da27e340789667c8898c0818147b7a4b49bcd8"},"schema_version":"1.0"},"canonical_sha256":"4b4bdc470cb93d1c16dbafff7aa22d0aa18eafe808a42f51b43000f2bd803964","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:33.852527Z","signature_b64":"uzU1P4x16mdHK3NRa4XU0W4byNydX0lgE5kQ6oPDFTFY6vM1ITnvFR7mv7OIVl7joAbi/8ISsGLwOZl32TddDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b4bdc470cb93d1c16dbafff7aa22d0aa18eafe808a42f51b43000f2bd803964","last_reissued_at":"2026-05-18T01:28:33.852043Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:33.852043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.00112","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:28:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Ha8PE66FORCsuMy0mP054fNQLI1psk7b0rRFJRvtvwVuDwnB/rnVzffO4rWVJPDbByGhlhnILUT3lIs7sElCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:15:47.089725Z"},"content_sha256":"97a9f58811f0551f1bbde7d0ac5ff0bc51005a64af88df91ffe6af975b602920","schema_version":"1.0","event_id":"sha256:97a9f58811f0551f1bbde7d0ac5ff0bc51005a64af88df91ffe6af975b602920"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JNF5YRYMXE6RYFW3V77XVIRNBK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher-order asymptotics for the parametric complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","stat.ME","stat.ML"],"primary_cat":"cs.IT","authors_text":"James G. Dowty","submitted_at":"2015-10-01T05:42:25Z","abstract_excerpt":"The parametric complexity is the key quantity in the minimum description length (MDL) approach to statistical model selection. Rissanen and others have shown that the parametric complexity of a statistical model approaches a simple function of the Fisher information volume of the model as the sample size $n$ goes to infinity. This paper derives higher-order asymptotic expansions for the parametric complexity, in the case of exponential families and independent and identically distributed data. These higher-order approximations are calculated for some examples and are shown to have better finit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00112","kind":"arxiv","version":3},"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":"2026-05-18T01:28:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qhd8H1TlGOApMkfeDDYGToHbllAgs1ftqLWm/hEvnQ2xkrOKheq5fwyJzUmOKTsGts6KRmb0VKkK/I5myDhJDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:15:47.090079Z"},"content_sha256":"4e538fbcbc4ecfd97f0178e9ff9979cc83df825c3179b9b2eb62ba75ddbf014c","schema_version":"1.0","event_id":"sha256:4e538fbcbc4ecfd97f0178e9ff9979cc83df825c3179b9b2eb62ba75ddbf014c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JNF5YRYMXE6RYFW3V77XVIRNBK/bundle.json","state_url":"https://pith.science/pith/JNF5YRYMXE6RYFW3V77XVIRNBK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JNF5YRYMXE6RYFW3V77XVIRNBK/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":"2026-06-03T17:15:47Z","links":{"resolver":"https://pith.science/pith/JNF5YRYMXE6RYFW3V77XVIRNBK","bundle":"https://pith.science/pith/JNF5YRYMXE6RYFW3V77XVIRNBK/bundle.json","state":"https://pith.science/pith/JNF5YRYMXE6RYFW3V77XVIRNBK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JNF5YRYMXE6RYFW3V77XVIRNBK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JNF5YRYMXE6RYFW3V77XVIRNBK","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":"56efe983b64db0593753c24196da27e340789667c8898c0818147b7a4b49bcd8","cross_cats_sorted":["math.IT","stat.ME","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-01T05:42:25Z","title_canon_sha256":"741221aec2c6222fa808776c90ca7c713c73daa03464ecee683d02501edac9be"},"schema_version":"1.0","source":{"id":"1510.00112","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.00112","created_at":"2026-05-18T01:28:33Z"},{"alias_kind":"arxiv_version","alias_value":"1510.00112v3","created_at":"2026-05-18T01:28:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00112","created_at":"2026-05-18T01:28:33Z"},{"alias_kind":"pith_short_12","alias_value":"JNF5YRYMXE6R","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JNF5YRYMXE6RYFW3","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JNF5YRYM","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:4e538fbcbc4ecfd97f0178e9ff9979cc83df825c3179b9b2eb62ba75ddbf014c","target":"graph","created_at":"2026-05-18T01:28:33Z","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":"The parametric complexity is the key quantity in the minimum description length (MDL) approach to statistical model selection. Rissanen and others have shown that the parametric complexity of a statistical model approaches a simple function of the Fisher information volume of the model as the sample size $n$ goes to infinity. This paper derives higher-order asymptotic expansions for the parametric complexity, in the case of exponential families and independent and identically distributed data. These higher-order approximations are calculated for some examples and are shown to have better finit","authors_text":"James G. Dowty","cross_cats":["math.IT","stat.ME","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-01T05:42:25Z","title":"Higher-order asymptotics for the parametric complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00112","kind":"arxiv","version":3},"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":"sha256:97a9f58811f0551f1bbde7d0ac5ff0bc51005a64af88df91ffe6af975b602920","target":"record","created_at":"2026-05-18T01:28:33Z","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":"56efe983b64db0593753c24196da27e340789667c8898c0818147b7a4b49bcd8","cross_cats_sorted":["math.IT","stat.ME","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-01T05:42:25Z","title_canon_sha256":"741221aec2c6222fa808776c90ca7c713c73daa03464ecee683d02501edac9be"},"schema_version":"1.0","source":{"id":"1510.00112","kind":"arxiv","version":3}},"canonical_sha256":"4b4bdc470cb93d1c16dbafff7aa22d0aa18eafe808a42f51b43000f2bd803964","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b4bdc470cb93d1c16dbafff7aa22d0aa18eafe808a42f51b43000f2bd803964","first_computed_at":"2026-05-18T01:28:33.852043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:33.852043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uzU1P4x16mdHK3NRa4XU0W4byNydX0lgE5kQ6oPDFTFY6vM1ITnvFR7mv7OIVl7joAbi/8ISsGLwOZl32TddDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:33.852527Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.00112","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97a9f58811f0551f1bbde7d0ac5ff0bc51005a64af88df91ffe6af975b602920","sha256:4e538fbcbc4ecfd97f0178e9ff9979cc83df825c3179b9b2eb62ba75ddbf014c"],"state_sha256":"42b944b4dbfe028bcc3aaa4e909b6284d72e2134ff989ee4b42db44253d2c99e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BDP/OVzPb/75CNTig/wPnsU494FPqZIGL9DpESdkGuIkbsJtxY2fllsaavL0hICIqNBwpw7WbDBJXVtOYG+rDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T17:15:47.092107Z","bundle_sha256":"fe84d08782573e686982924e2c41cb4aa61e8bac9f11a01e4579062f36d403c4"}}