{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:NTVFLTBIJX6SXKAKIGCXUDD7HY","short_pith_number":"pith:NTVFLTBI","canonical_record":{"source":{"id":"1411.4977","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-11-18T19:40:50Z","cross_cats_sorted":[],"title_canon_sha256":"b81a33ecbeeacb856e08e8e8b13244372f849195595225e9821a01752311e33a","abstract_canon_sha256":"ba24da6836307962b786c539dac7a4da1a491b35f295dacad492c6ae5bf886c3"},"schema_version":"1.0"},"canonical_sha256":"6cea55cc284dfd2ba80a41857a0c7f3e05dd07a4556b7ebd87bce4f2b91c4c6b","source":{"kind":"arxiv","id":"1411.4977","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4977","created_at":"2026-05-18T01:20:56Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4977v3","created_at":"2026-05-18T01:20:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4977","created_at":"2026-05-18T01:20:56Z"},{"alias_kind":"pith_short_12","alias_value":"NTVFLTBIJX6S","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NTVFLTBIJX6SXKAK","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NTVFLTBI","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:NTVFLTBIJX6SXKAKIGCXUDD7HY","target":"record","payload":{"canonical_record":{"source":{"id":"1411.4977","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-11-18T19:40:50Z","cross_cats_sorted":[],"title_canon_sha256":"b81a33ecbeeacb856e08e8e8b13244372f849195595225e9821a01752311e33a","abstract_canon_sha256":"ba24da6836307962b786c539dac7a4da1a491b35f295dacad492c6ae5bf886c3"},"schema_version":"1.0"},"canonical_sha256":"6cea55cc284dfd2ba80a41857a0c7f3e05dd07a4556b7ebd87bce4f2b91c4c6b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:56.149965Z","signature_b64":"X2D4rSlHCjvI8A8Z+wVXzdxE7vlcPWqzWd/nE1aqSOJBlVJ/V4nUvDgkYOVAFRPvESbKQcqDT6FtLMNanJmGBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cea55cc284dfd2ba80a41857a0c7f3e05dd07a4556b7ebd87bce4f2b91c4c6b","last_reissued_at":"2026-05-18T01:20:56.149436Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:56.149436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.4977","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":"2026-05-18T01:20:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4JVRcNg1r5seeBRo/cnx1r/l/65jGx5lxP68G6vmE0Bpy72WnG8L42UN0p7jrgGfnozMlAodu3+gDJGnaZfkCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T13:06:54.150685Z"},"content_sha256":"09f0d3d1816c5a63fb3a545b43dacc140c8a5cc91a320d856c7cd707b400fd93","schema_version":"1.0","event_id":"sha256:09f0d3d1816c5a63fb3a545b43dacc140c8a5cc91a320d856c7cd707b400fd93"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:NTVFLTBIJX6SXKAKIGCXUDD7HY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cyclicity and invariant subspaces in the Dirichlet spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Karim Kellay (IMB), Omar El-Fallah, Youssef Elmadani","submitted_at":"2014-11-18T19:40:50Z","abstract_excerpt":"Let $\\mu$ be a positive finite measure on the unit circle and $\\mathcal{D} (\\mu)$  the associated Dirichlet  space. The generalized Brown-Shields conjecture asserts that an  outer function $f \\in \\mathcal{D} (\\mu )$ is cyclic if and only if $c\\_\\mu (Z (f))= 0$, where $c\\_\\mu$ is the   capacity associated with $\\mathcal{D} (\\mu)$ and $Z(f)$ is the zero set of $f$. In this paper we prove that this conjecture is true for measures with countable support. We also give in this case a  complete and explicit characterization of  invariant subspaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4977","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":"2026-05-18T01:20:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+UX0BNuGgRScLEfUdgwV9kUHD60L+VhtoFeILe10kwtTiu7FVmzUY9F3RYdPGaJK3y6OLIfNr6JPdTTADuUMAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T13:06:54.151034Z"},"content_sha256":"a913761936cdbcbbcfd5ef35224d20b9d09a9239d759a36def04f0650d522914","schema_version":"1.0","event_id":"sha256:a913761936cdbcbbcfd5ef35224d20b9d09a9239d759a36def04f0650d522914"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NTVFLTBIJX6SXKAKIGCXUDD7HY/bundle.json","state_url":"https://pith.science/pith/NTVFLTBIJX6SXKAKIGCXUDD7HY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NTVFLTBIJX6SXKAKIGCXUDD7HY/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":"2026-06-05T13:06:54Z","links":{"resolver":"https://pith.science/pith/NTVFLTBIJX6SXKAKIGCXUDD7HY","bundle":"https://pith.science/pith/NTVFLTBIJX6SXKAKIGCXUDD7HY/bundle.json","state":"https://pith.science/pith/NTVFLTBIJX6SXKAKIGCXUDD7HY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NTVFLTBIJX6SXKAKIGCXUDD7HY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NTVFLTBIJX6SXKAKIGCXUDD7HY","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":"ba24da6836307962b786c539dac7a4da1a491b35f295dacad492c6ae5bf886c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-11-18T19:40:50Z","title_canon_sha256":"b81a33ecbeeacb856e08e8e8b13244372f849195595225e9821a01752311e33a"},"schema_version":"1.0","source":{"id":"1411.4977","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4977","created_at":"2026-05-18T01:20:56Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4977v3","created_at":"2026-05-18T01:20:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4977","created_at":"2026-05-18T01:20:56Z"},{"alias_kind":"pith_short_12","alias_value":"NTVFLTBIJX6S","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NTVFLTBIJX6SXKAK","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NTVFLTBI","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:a913761936cdbcbbcfd5ef35224d20b9d09a9239d759a36def04f0650d522914","target":"graph","created_at":"2026-05-18T01:20:56Z","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":"Let $\\mu$ be a positive finite measure on the unit circle and $\\mathcal{D} (\\mu)$  the associated Dirichlet  space. The generalized Brown-Shields conjecture asserts that an  outer function $f \\in \\mathcal{D} (\\mu )$ is cyclic if and only if $c\\_\\mu (Z (f))= 0$, where $c\\_\\mu$ is the   capacity associated with $\\mathcal{D} (\\mu)$ and $Z(f)$ is the zero set of $f$. In this paper we prove that this conjecture is true for measures with countable support. We also give in this case a  complete and explicit characterization of  invariant subspaces.","authors_text":"Karim Kellay (IMB), Omar El-Fallah, Youssef Elmadani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-11-18T19:40:50Z","title":"Cyclicity and invariant subspaces in the Dirichlet spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4977","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":"sha256:09f0d3d1816c5a63fb3a545b43dacc140c8a5cc91a320d856c7cd707b400fd93","target":"record","created_at":"2026-05-18T01:20:56Z","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":"ba24da6836307962b786c539dac7a4da1a491b35f295dacad492c6ae5bf886c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-11-18T19:40:50Z","title_canon_sha256":"b81a33ecbeeacb856e08e8e8b13244372f849195595225e9821a01752311e33a"},"schema_version":"1.0","source":{"id":"1411.4977","kind":"arxiv","version":3}},"canonical_sha256":"6cea55cc284dfd2ba80a41857a0c7f3e05dd07a4556b7ebd87bce4f2b91c4c6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cea55cc284dfd2ba80a41857a0c7f3e05dd07a4556b7ebd87bce4f2b91c4c6b","first_computed_at":"2026-05-18T01:20:56.149436Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:56.149436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X2D4rSlHCjvI8A8Z+wVXzdxE7vlcPWqzWd/nE1aqSOJBlVJ/V4nUvDgkYOVAFRPvESbKQcqDT6FtLMNanJmGBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:56.149965Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.4977","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09f0d3d1816c5a63fb3a545b43dacc140c8a5cc91a320d856c7cd707b400fd93","sha256:a913761936cdbcbbcfd5ef35224d20b9d09a9239d759a36def04f0650d522914"],"state_sha256":"c2c8b658031f459297e8bc54d9706ead62e75f588bb72572e01026e6601928df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8zQw+tX/ZGNRacYn01k2PSjQyXJZuAxSG3UbDA3bVLnUZkK7a9SGYl6DBPF3WmFQTZ5YHjOSS6nijS09S+6vAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T13:06:54.152979Z","bundle_sha256":"aca71b048ab1891c7a57176f34db6457a16e1f25161b0466b30e98b8331b7a44"}}