{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:L7NNJLOMHRSFACWHTFTOHDJTBZ","short_pith_number":"pith:L7NNJLOM","canonical_record":{"source":{"id":"1409.3309","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-09-11T03:29:43Z","cross_cats_sorted":[],"title_canon_sha256":"508b52180876aba84b91b1d625807576433fd8f7de81435efd7768c0f9fc0b7d","abstract_canon_sha256":"4c7f14e28ab68f83d085d63aa0af2521f85bf4e51e54abd8ed163608c27ad3a4"},"schema_version":"1.0"},"canonical_sha256":"5fdad4adcc3c64500ac79966e38d330e7ded7ac26df4c26a94b5fc5be7af9561","source":{"kind":"arxiv","id":"1409.3309","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3309","created_at":"2026-05-18T02:43:01Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3309v1","created_at":"2026-05-18T02:43:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3309","created_at":"2026-05-18T02:43:01Z"},{"alias_kind":"pith_short_12","alias_value":"L7NNJLOMHRSF","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"L7NNJLOMHRSFACWH","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"L7NNJLOM","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:L7NNJLOMHRSFACWHTFTOHDJTBZ","target":"record","payload":{"canonical_record":{"source":{"id":"1409.3309","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-09-11T03:29:43Z","cross_cats_sorted":[],"title_canon_sha256":"508b52180876aba84b91b1d625807576433fd8f7de81435efd7768c0f9fc0b7d","abstract_canon_sha256":"4c7f14e28ab68f83d085d63aa0af2521f85bf4e51e54abd8ed163608c27ad3a4"},"schema_version":"1.0"},"canonical_sha256":"5fdad4adcc3c64500ac79966e38d330e7ded7ac26df4c26a94b5fc5be7af9561","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:01.683961Z","signature_b64":"3cssKfNSr8OX7bSVW97MqZVikzrDQkQUVWE/FJZsdBtcahDxSTXOYiHCAV6fYm0+x2ht51mO+tER9GKn4on1AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fdad4adcc3c64500ac79966e38d330e7ded7ac26df4c26a94b5fc5be7af9561","last_reissued_at":"2026-05-18T02:43:01.683394Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:01.683394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.3309","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":"2026-05-18T02:43:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bhCc8SiASPsOuFOOrpvWlTrfrCD/hT6wqI7BnFrvR1eig/8EbdcqR+nwk+1gNIS/ZDUBp4voXWtXD3BJFLEYDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:56:17.967096Z"},"content_sha256":"8bdecb824eaf298e826a33ca65d27bc9424041198a8038844274f807b1e1ebd3","schema_version":"1.0","event_id":"sha256:8bdecb824eaf298e826a33ca65d27bc9424041198a8038844274f807b1e1ebd3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:L7NNJLOMHRSFACWHTFTOHDJTBZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conjugacies provided by fractal transformations I : Conjugate measures, Hilbert spaces, orthogonal expansions, and flows, on self-referential spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Andrew Vince, Christoph Bandt, Markus Hegland, Michael Barnsley","submitted_at":"2014-09-11T03:29:43Z","abstract_excerpt":"Theorems and explicit examples are used to show how transformations between self-similar sets (general sense) may be continuous almost everywhere with respect to stationary measures on the sets and may be used to carry well known flows and spectral analysis over from familiar settings to new ones. The focus of this work is on a number of surprising applications including (i) what we call fractal Fourier analysis, in which the graphs of the basis functions are Cantor sets, being discontinuous at a countable dense set of points, yet have very good approximation properties; (ii) Lebesgue measure-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3309","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":"2026-05-18T02:43:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aV2KlO2EU5c/xOlZZVjIt/EB8ZRo9Vokg9vexfJZqDcAjijb4XjedFV5i1O1KdVAAXVXP+PAFhovTb+V87LCAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:56:17.967780Z"},"content_sha256":"78150d8c9e84af425619c3e2bd16e8757996ccf7cd2828f8bf9c52e6a265e3c9","schema_version":"1.0","event_id":"sha256:78150d8c9e84af425619c3e2bd16e8757996ccf7cd2828f8bf9c52e6a265e3c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L7NNJLOMHRSFACWHTFTOHDJTBZ/bundle.json","state_url":"https://pith.science/pith/L7NNJLOMHRSFACWHTFTOHDJTBZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L7NNJLOMHRSFACWHTFTOHDJTBZ/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":"2026-06-07T16:56:17Z","links":{"resolver":"https://pith.science/pith/L7NNJLOMHRSFACWHTFTOHDJTBZ","bundle":"https://pith.science/pith/L7NNJLOMHRSFACWHTFTOHDJTBZ/bundle.json","state":"https://pith.science/pith/L7NNJLOMHRSFACWHTFTOHDJTBZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L7NNJLOMHRSFACWHTFTOHDJTBZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:L7NNJLOMHRSFACWHTFTOHDJTBZ","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":"4c7f14e28ab68f83d085d63aa0af2521f85bf4e51e54abd8ed163608c27ad3a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-09-11T03:29:43Z","title_canon_sha256":"508b52180876aba84b91b1d625807576433fd8f7de81435efd7768c0f9fc0b7d"},"schema_version":"1.0","source":{"id":"1409.3309","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3309","created_at":"2026-05-18T02:43:01Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3309v1","created_at":"2026-05-18T02:43:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3309","created_at":"2026-05-18T02:43:01Z"},{"alias_kind":"pith_short_12","alias_value":"L7NNJLOMHRSF","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"L7NNJLOMHRSFACWH","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"L7NNJLOM","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:78150d8c9e84af425619c3e2bd16e8757996ccf7cd2828f8bf9c52e6a265e3c9","target":"graph","created_at":"2026-05-18T02:43:01Z","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":"Theorems and explicit examples are used to show how transformations between self-similar sets (general sense) may be continuous almost everywhere with respect to stationary measures on the sets and may be used to carry well known flows and spectral analysis over from familiar settings to new ones. The focus of this work is on a number of surprising applications including (i) what we call fractal Fourier analysis, in which the graphs of the basis functions are Cantor sets, being discontinuous at a countable dense set of points, yet have very good approximation properties; (ii) Lebesgue measure-","authors_text":"Andrew Vince, Christoph Bandt, Markus Hegland, Michael Barnsley","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-09-11T03:29:43Z","title":"Conjugacies provided by fractal transformations I : Conjugate measures, Hilbert spaces, orthogonal expansions, and flows, on self-referential spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3309","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":"sha256:8bdecb824eaf298e826a33ca65d27bc9424041198a8038844274f807b1e1ebd3","target":"record","created_at":"2026-05-18T02:43:01Z","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":"4c7f14e28ab68f83d085d63aa0af2521f85bf4e51e54abd8ed163608c27ad3a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-09-11T03:29:43Z","title_canon_sha256":"508b52180876aba84b91b1d625807576433fd8f7de81435efd7768c0f9fc0b7d"},"schema_version":"1.0","source":{"id":"1409.3309","kind":"arxiv","version":1}},"canonical_sha256":"5fdad4adcc3c64500ac79966e38d330e7ded7ac26df4c26a94b5fc5be7af9561","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fdad4adcc3c64500ac79966e38d330e7ded7ac26df4c26a94b5fc5be7af9561","first_computed_at":"2026-05-18T02:43:01.683394Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:01.683394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3cssKfNSr8OX7bSVW97MqZVikzrDQkQUVWE/FJZsdBtcahDxSTXOYiHCAV6fYm0+x2ht51mO+tER9GKn4on1AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:01.683961Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.3309","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8bdecb824eaf298e826a33ca65d27bc9424041198a8038844274f807b1e1ebd3","sha256:78150d8c9e84af425619c3e2bd16e8757996ccf7cd2828f8bf9c52e6a265e3c9"],"state_sha256":"25827ade8667b7ed841c5327d08bb00c02c81ee3b1981b00381cc61a3e2132d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mZqKf9jbqT1XjpOxrqpy2E4ppiiJZsIWMkre7DKPi8D94TrNSF7rTW0ie2ot8l9mCKxu/5fEVHewl2Ue9uZBBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:56:17.972286Z","bundle_sha256":"38f448f243b0ad7e450a8cf506ac5f3f1d0b0bd41d0b70681b07349f15399eac"}}