{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SXZBIB24RDRMH5AZPSQ2EGYBJH","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":"e7d98e43a67aad3514468df0ee5ed1fb8b4eabe1cfc2ee8bbcda275b52f6b065","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-15T17:12:06Z","title_canon_sha256":"1dbb157c09e667a48e884d2571766747a989cb315c703bf956d44a86ecf2266d"},"schema_version":"1.0","source":{"id":"1606.04866","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.04866","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"1606.04866v2","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.04866","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"SXZBIB24RDRM","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SXZBIB24RDRMH5AZ","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SXZBIB24","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:51cbade2697d98cb0599fc54fd4033c7fcbcba34d730f0cb263bb62f7cf815f3","target":"graph","created_at":"2026-05-18T01:04:49Z","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":"We study certain infinite-dimensional probability measures in connection with frame analysis. Earlier work on frame-measures has so far focused on the case of finite-dimensional frames. We point out that there are good reasons for a sharp distinction between stochastic analysis involving frames in finite vs infinite dimensions. For the case of infinite-dimensional Hilbert space $\\mathcal{H}$, we study three cases of measures. We first show that, for $\\mathcal{H}$ infinite dimensional, 1 one must resort to infinite dimensional measure spaces which properly contain $\\mathcal{H}$. The three cases","authors_text":"Myung-Sin Song, Palle E. T. Jorgensen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-15T17:12:06Z","title":"Infinite-Dimensional Measure Spaces and Frame Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04866","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":"sha256:329a7e5aba4628fdfbf141c35aebe097e6e4865537d4e709093650eb483a0a04","target":"record","created_at":"2026-05-18T01:04:49Z","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":"e7d98e43a67aad3514468df0ee5ed1fb8b4eabe1cfc2ee8bbcda275b52f6b065","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-15T17:12:06Z","title_canon_sha256":"1dbb157c09e667a48e884d2571766747a989cb315c703bf956d44a86ecf2266d"},"schema_version":"1.0","source":{"id":"1606.04866","kind":"arxiv","version":2}},"canonical_sha256":"95f214075c88e2c3f4197ca1a21b0149c50f7d0516f9b77f990f9196d4aab039","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95f214075c88e2c3f4197ca1a21b0149c50f7d0516f9b77f990f9196d4aab039","first_computed_at":"2026-05-18T01:04:49.676564Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:49.676564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yFhqH49ED+qwlTP/a/SHFbirjl/azH0YvKqqltB7+3Lu0ooAhF3HjMJfJoyx8cvz6W9NIA1+dNzfgH69rCU8BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:49.677041Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.04866","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:329a7e5aba4628fdfbf141c35aebe097e6e4865537d4e709093650eb483a0a04","sha256:51cbade2697d98cb0599fc54fd4033c7fcbcba34d730f0cb263bb62f7cf815f3"],"state_sha256":"577f18882c62d994344dc5bbada6afa7506d314d35a6555feccecfcc4b970402"}