{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7Z6F72U3EIF3EXHO2H6ZDCVG54","short_pith_number":"pith:7Z6F72U3","canonical_record":{"source":{"id":"1409.7482","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-09-26T06:50:22Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"8e2fdaa0e48ea3e7f34b70a3da7cf7cacd88a384db263c19afff230d1786e4cc","abstract_canon_sha256":"1f60559ffaaefc1638be516a1ab6218f2ce92e406175d1467fcade0961bb923c"},"schema_version":"1.0"},"canonical_sha256":"fe7c5fea9b220bb25ceed1fd918aa6ef17cd08ef0f5e7157e587ea9dbd1579b1","source":{"kind":"arxiv","id":"1409.7482","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7482","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7482v1","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7482","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"7Z6F72U3EIF3","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7Z6F72U3EIF3EXHO","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7Z6F72U3","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7Z6F72U3EIF3EXHO2H6ZDCVG54","target":"record","payload":{"canonical_record":{"source":{"id":"1409.7482","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-09-26T06:50:22Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"8e2fdaa0e48ea3e7f34b70a3da7cf7cacd88a384db263c19afff230d1786e4cc","abstract_canon_sha256":"1f60559ffaaefc1638be516a1ab6218f2ce92e406175d1467fcade0961bb923c"},"schema_version":"1.0"},"canonical_sha256":"fe7c5fea9b220bb25ceed1fd918aa6ef17cd08ef0f5e7157e587ea9dbd1579b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:52.574097Z","signature_b64":"Quy3eQ8BuLM/wvwHbMzuxFFx9yDS4DAQSsDN1BKAX9T2xEuZEB2e/amX3Nbx0cvTqQqp55f2ifVSi3VuLePBCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe7c5fea9b220bb25ceed1fd918aa6ef17cd08ef0f5e7157e587ea9dbd1579b1","last_reissued_at":"2026-05-18T02:41:52.573507Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:52.573507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.7482","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":"2026-05-18T02:41:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qcgMuZuAOVCRtJHMMIvta9JI5GREgYAkCcOg5H4FjdhA4GvxbSyJueXOlK6FlT/LlMXFNTNYtGcSUrtkdGPMAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T13:30:07.690869Z"},"content_sha256":"ab8cbd2806af36c347b0d9ecb8e63525bce54cfe95c75c15969bb1951d83b447","schema_version":"1.0","event_id":"sha256:ab8cbd2806af36c347b0d9ecb8e63525bce54cfe95c75c15969bb1951d83b447"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7Z6F72U3EIF3EXHO2H6ZDCVG54","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discrete Dispersion Models and Their Tweedie Asymptotics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Bent J{\\o}rgensen, C\\'elestin C. Kokonendji","submitted_at":"2014-09-26T06:50:22Z","abstract_excerpt":"We introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The equidispersed Poisson model has a special place in this approach, whereas several overdispersed discrete distributions, such as the Neyman Type A, P\\'olya-Aeppli, negative binomial and Poisson-inverse Gaussian, turn out to be Poisson-Tweedie factorial dispersion models with power dispersion functions, analogous to ordinary Tweedie exponential dispersion models with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7482","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":"2026-05-18T02:41:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EVUkfz5FrBvv9iTK78KNuJsq8QvnaXEnryIlIsuaGt+jaW+16kV8i1WEY6CF8m1mpnmTQ0UahrGG3jUa3JAYBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T13:30:07.691228Z"},"content_sha256":"da36c57b8504d035f06c2fa6b4fcd8f8e9b0c598165fa7cac324ee71555e0e4c","schema_version":"1.0","event_id":"sha256:da36c57b8504d035f06c2fa6b4fcd8f8e9b0c598165fa7cac324ee71555e0e4c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7Z6F72U3EIF3EXHO2H6ZDCVG54/bundle.json","state_url":"https://pith.science/pith/7Z6F72U3EIF3EXHO2H6ZDCVG54/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7Z6F72U3EIF3EXHO2H6ZDCVG54/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":"2026-06-25T13:30:07Z","links":{"resolver":"https://pith.science/pith/7Z6F72U3EIF3EXHO2H6ZDCVG54","bundle":"https://pith.science/pith/7Z6F72U3EIF3EXHO2H6ZDCVG54/bundle.json","state":"https://pith.science/pith/7Z6F72U3EIF3EXHO2H6ZDCVG54/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7Z6F72U3EIF3EXHO2H6ZDCVG54/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7Z6F72U3EIF3EXHO2H6ZDCVG54","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":"1f60559ffaaefc1638be516a1ab6218f2ce92e406175d1467fcade0961bb923c","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-09-26T06:50:22Z","title_canon_sha256":"8e2fdaa0e48ea3e7f34b70a3da7cf7cacd88a384db263c19afff230d1786e4cc"},"schema_version":"1.0","source":{"id":"1409.7482","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7482","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7482v1","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7482","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"7Z6F72U3EIF3","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7Z6F72U3EIF3EXHO","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7Z6F72U3","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:da36c57b8504d035f06c2fa6b4fcd8f8e9b0c598165fa7cac324ee71555e0e4c","target":"graph","created_at":"2026-05-18T02:41:52Z","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 introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The equidispersed Poisson model has a special place in this approach, whereas several overdispersed discrete distributions, such as the Neyman Type A, P\\'olya-Aeppli, negative binomial and Poisson-inverse Gaussian, turn out to be Poisson-Tweedie factorial dispersion models with power dispersion functions, analogous to ordinary Tweedie exponential dispersion models with ","authors_text":"Bent J{\\o}rgensen, C\\'elestin C. Kokonendji","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-09-26T06:50:22Z","title":"Discrete Dispersion Models and Their Tweedie Asymptotics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7482","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:ab8cbd2806af36c347b0d9ecb8e63525bce54cfe95c75c15969bb1951d83b447","target":"record","created_at":"2026-05-18T02:41:52Z","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":"1f60559ffaaefc1638be516a1ab6218f2ce92e406175d1467fcade0961bb923c","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-09-26T06:50:22Z","title_canon_sha256":"8e2fdaa0e48ea3e7f34b70a3da7cf7cacd88a384db263c19afff230d1786e4cc"},"schema_version":"1.0","source":{"id":"1409.7482","kind":"arxiv","version":1}},"canonical_sha256":"fe7c5fea9b220bb25ceed1fd918aa6ef17cd08ef0f5e7157e587ea9dbd1579b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe7c5fea9b220bb25ceed1fd918aa6ef17cd08ef0f5e7157e587ea9dbd1579b1","first_computed_at":"2026-05-18T02:41:52.573507Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:52.573507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Quy3eQ8BuLM/wvwHbMzuxFFx9yDS4DAQSsDN1BKAX9T2xEuZEB2e/amX3Nbx0cvTqQqp55f2ifVSi3VuLePBCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:52.574097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.7482","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab8cbd2806af36c347b0d9ecb8e63525bce54cfe95c75c15969bb1951d83b447","sha256:da36c57b8504d035f06c2fa6b4fcd8f8e9b0c598165fa7cac324ee71555e0e4c"],"state_sha256":"a1d1683c3de6ca434d0f817ec5024bf50c5353d828906d039d1082c98557e50d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yWZNikw862HH2289Yrc5x94HbpljzL2hltXvWudqBU1CjN4bzGtr7jUytH/1Ko0niCO9i+LI0wDQRNU+BcHOCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T13:30:07.693303Z","bundle_sha256":"30a8d6b23768dc9fc1d7b4ed19673bbf4dfe79322606a3b70b9a8414475b94f5"}}