{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:TRXDFQXDDKRXTL3BV7M2JKR6HU","short_pith_number":"pith:TRXDFQXD","canonical_record":{"source":{"id":"1402.4147","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-17T21:12:41Z","cross_cats_sorted":[],"title_canon_sha256":"3f64615024fc1e366adab6560f1576be17693f765f6e34432a228ebd5130141b","abstract_canon_sha256":"ee55605a7f4fac7bbdf998c643cf6c8e769b7863f5e22e1dd961ac16b25d8f1e"},"schema_version":"1.0"},"canonical_sha256":"9c6e32c2e31aa379af61afd9a4aa3e3d1dd3e708de2966eeb4e2bebcd98a4d5b","source":{"kind":"arxiv","id":"1402.4147","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.4147","created_at":"2026-05-18T02:58:44Z"},{"alias_kind":"arxiv_version","alias_value":"1402.4147v1","created_at":"2026-05-18T02:58:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4147","created_at":"2026-05-18T02:58:44Z"},{"alias_kind":"pith_short_12","alias_value":"TRXDFQXDDKRX","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"TRXDFQXDDKRXTL3B","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"TRXDFQXD","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:TRXDFQXDDKRXTL3BV7M2JKR6HU","target":"record","payload":{"canonical_record":{"source":{"id":"1402.4147","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-17T21:12:41Z","cross_cats_sorted":[],"title_canon_sha256":"3f64615024fc1e366adab6560f1576be17693f765f6e34432a228ebd5130141b","abstract_canon_sha256":"ee55605a7f4fac7bbdf998c643cf6c8e769b7863f5e22e1dd961ac16b25d8f1e"},"schema_version":"1.0"},"canonical_sha256":"9c6e32c2e31aa379af61afd9a4aa3e3d1dd3e708de2966eeb4e2bebcd98a4d5b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:44.715879Z","signature_b64":"yB3Z/PyJaxlooq4HtCY73gk1ryhV1RgUBNgJXUG+rwidDLKpwk85ru4iFsZvr5HgCxgw9m6XfNVTN3Is6rMADQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c6e32c2e31aa379af61afd9a4aa3e3d1dd3e708de2966eeb4e2bebcd98a4d5b","last_reissued_at":"2026-05-18T02:58:44.715266Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:44.715266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.4147","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":"2026-05-18T02:58:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jOSVhx7N+m9/2nHElBsLLl/eTLbHnQbc1ZuHjhPEPQ0jB+eqKEtHseP/ekRqZjpKch1EVpsHSRQOzR9qvYWzAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:47:02.461156Z"},"content_sha256":"852a5c74df5253f92dae079cdf17d41d962c58e23094d5701492e498f785af85","schema_version":"1.0","event_id":"sha256:852a5c74df5253f92dae079cdf17d41d962c58e23094d5701492e498f785af85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:TRXDFQXDDKRXTL3BV7M2JKR6HU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fixed points of multivariate smoothing transforms with scalar weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Iksanov, Matthias Meiners","submitted_at":"2014-02-17T21:12:41Z","abstract_excerpt":"Given a sequence $(C_1,\\ldots,C_d,T_1,T_2,\\ldots)$ of real-valued random variables with $N := \\#\\{j \\geq 1: T_j \\not = 0\\} < \\infty$ almost surely, there is an associated smoothing transformation which maps a distribution $P$ on $\\mathbb{R}^d$ to the distribution of $\\sum_{j \\geq 1} T_j \\mathbf{X}^{(j)} + \\mathbf{C}$ where $\\mathbf{C} = (C_1,\\ldots,C_d)$ and $(\\mathbf{X}^{(j)})_{j \\geq 1}$ is a sequence of independent random vectors with distribution $P$ independent of $(C_1,\\ldots,C_d,T_1,T_2,\\ldots)$. We are interested in the fixed points of this mapping. By improving on the techniques devel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4147","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":"2026-05-18T02:58:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Zvq5xr4xZBrbNg2cRZBAEhsxjBfy1nF5tomf8chH1YBtjga88ztwosFapCrtD3ChC/aZP7EDsgHfw+2WuURDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:47:02.461528Z"},"content_sha256":"d2cc07e12331c39e8ddccfd364c737a2d2f92d1500e3dcaf1785c1ac45e0dfbf","schema_version":"1.0","event_id":"sha256:d2cc07e12331c39e8ddccfd364c737a2d2f92d1500e3dcaf1785c1ac45e0dfbf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TRXDFQXDDKRXTL3BV7M2JKR6HU/bundle.json","state_url":"https://pith.science/pith/TRXDFQXDDKRXTL3BV7M2JKR6HU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TRXDFQXDDKRXTL3BV7M2JKR6HU/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":"2026-05-30T22:47:02Z","links":{"resolver":"https://pith.science/pith/TRXDFQXDDKRXTL3BV7M2JKR6HU","bundle":"https://pith.science/pith/TRXDFQXDDKRXTL3BV7M2JKR6HU/bundle.json","state":"https://pith.science/pith/TRXDFQXDDKRXTL3BV7M2JKR6HU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TRXDFQXDDKRXTL3BV7M2JKR6HU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TRXDFQXDDKRXTL3BV7M2JKR6HU","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":"ee55605a7f4fac7bbdf998c643cf6c8e769b7863f5e22e1dd961ac16b25d8f1e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-17T21:12:41Z","title_canon_sha256":"3f64615024fc1e366adab6560f1576be17693f765f6e34432a228ebd5130141b"},"schema_version":"1.0","source":{"id":"1402.4147","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.4147","created_at":"2026-05-18T02:58:44Z"},{"alias_kind":"arxiv_version","alias_value":"1402.4147v1","created_at":"2026-05-18T02:58:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4147","created_at":"2026-05-18T02:58:44Z"},{"alias_kind":"pith_short_12","alias_value":"TRXDFQXDDKRX","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"TRXDFQXDDKRXTL3B","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"TRXDFQXD","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:d2cc07e12331c39e8ddccfd364c737a2d2f92d1500e3dcaf1785c1ac45e0dfbf","target":"graph","created_at":"2026-05-18T02:58:44Z","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":"Given a sequence $(C_1,\\ldots,C_d,T_1,T_2,\\ldots)$ of real-valued random variables with $N := \\#\\{j \\geq 1: T_j \\not = 0\\} < \\infty$ almost surely, there is an associated smoothing transformation which maps a distribution $P$ on $\\mathbb{R}^d$ to the distribution of $\\sum_{j \\geq 1} T_j \\mathbf{X}^{(j)} + \\mathbf{C}$ where $\\mathbf{C} = (C_1,\\ldots,C_d)$ and $(\\mathbf{X}^{(j)})_{j \\geq 1}$ is a sequence of independent random vectors with distribution $P$ independent of $(C_1,\\ldots,C_d,T_1,T_2,\\ldots)$. We are interested in the fixed points of this mapping. By improving on the techniques devel","authors_text":"Alexander Iksanov, Matthias Meiners","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-17T21:12:41Z","title":"Fixed points of multivariate smoothing transforms with scalar weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4147","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":"sha256:852a5c74df5253f92dae079cdf17d41d962c58e23094d5701492e498f785af85","target":"record","created_at":"2026-05-18T02:58:44Z","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":"ee55605a7f4fac7bbdf998c643cf6c8e769b7863f5e22e1dd961ac16b25d8f1e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-17T21:12:41Z","title_canon_sha256":"3f64615024fc1e366adab6560f1576be17693f765f6e34432a228ebd5130141b"},"schema_version":"1.0","source":{"id":"1402.4147","kind":"arxiv","version":1}},"canonical_sha256":"9c6e32c2e31aa379af61afd9a4aa3e3d1dd3e708de2966eeb4e2bebcd98a4d5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c6e32c2e31aa379af61afd9a4aa3e3d1dd3e708de2966eeb4e2bebcd98a4d5b","first_computed_at":"2026-05-18T02:58:44.715266Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:44.715266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yB3Z/PyJaxlooq4HtCY73gk1ryhV1RgUBNgJXUG+rwidDLKpwk85ru4iFsZvr5HgCxgw9m6XfNVTN3Is6rMADQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:44.715879Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.4147","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:852a5c74df5253f92dae079cdf17d41d962c58e23094d5701492e498f785af85","sha256:d2cc07e12331c39e8ddccfd364c737a2d2f92d1500e3dcaf1785c1ac45e0dfbf"],"state_sha256":"c2b885034bb2d388158b0088362155a46f4b7bb4c749e64c059fdfb29c59f54b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AyBMbB0iAeRoWoIBf5sWB1cVEc84L6giJ+JruWWmz1oMLqN0j8OEDtT1bwD6pkx82u93xEKctXBAoBqIwZMIBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T22:47:02.463584Z","bundle_sha256":"9a2e31398c3777ccce94a32f4fac333e86acaaa83f823ae271d2ddd376fef5f4"}}