{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:SBLH32UFVOT7TVKX7OP3OZXLYF","short_pith_number":"pith:SBLH32UF","canonical_record":{"source":{"id":"1109.1091","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-09-06T07:14:40Z","cross_cats_sorted":[],"title_canon_sha256":"693e2790b029c941813751a8d5f9c82fa7cbf2a483f5007b9997d55f8fbe36ce","abstract_canon_sha256":"874796ebc02dca474dc015a84c25d7b0625693b461ef15ef702454a7b316a16f"},"schema_version":"1.0"},"canonical_sha256":"90567dea85aba7f9d557fb9fb766ebc15bc3844a5f96436de86919bfdccd8c2e","source":{"kind":"arxiv","id":"1109.1091","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1091","created_at":"2026-05-18T02:00:39Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1091v2","created_at":"2026-05-18T02:00:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1091","created_at":"2026-05-18T02:00:39Z"},{"alias_kind":"pith_short_12","alias_value":"SBLH32UFVOT7","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SBLH32UFVOT7TVKX","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SBLH32UF","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:SBLH32UFVOT7TVKX7OP3OZXLYF","target":"record","payload":{"canonical_record":{"source":{"id":"1109.1091","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-09-06T07:14:40Z","cross_cats_sorted":[],"title_canon_sha256":"693e2790b029c941813751a8d5f9c82fa7cbf2a483f5007b9997d55f8fbe36ce","abstract_canon_sha256":"874796ebc02dca474dc015a84c25d7b0625693b461ef15ef702454a7b316a16f"},"schema_version":"1.0"},"canonical_sha256":"90567dea85aba7f9d557fb9fb766ebc15bc3844a5f96436de86919bfdccd8c2e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:39.236926Z","signature_b64":"HIHjqcrUl/ajytM8IqkqUjTXSPPvwYyM7HB+CzwngyKbRaE1FOSGCideg/fmcVFVt/U1ApuANti8dlZkKxmyCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90567dea85aba7f9d557fb9fb766ebc15bc3844a5f96436de86919bfdccd8c2e","last_reissued_at":"2026-05-18T02:00:39.236272Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:39.236272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.1091","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:00:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7/iVHr1qe/lbxEI1Hdcd5zabSUXFwlaME48atPQOf2PRTcFBvCFt5ZBmpp0RJH9HtosfRkxkjA+CBNSGw6dGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:54:30.823075Z"},"content_sha256":"a63883772716d950035847b97c61654530274ccdbc2d890d50a23281e0f975bc","schema_version":"1.0","event_id":"sha256:a63883772716d950035847b97c61654530274ccdbc2d890d50a23281e0f975bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:SBLH32UFVOT7TVKX7OP3OZXLYF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bad boundary behavior in star invariant subspaces I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Andreas Hartmann (IMB), William T. Ross","submitted_at":"2011-09-06T07:14:40Z","abstract_excerpt":"We discuss the boundary behavior of functions in backward shift invariant subspaces $(B H^2)^{\\perp}$, where $B$ is a Blaschke product. Extending some results of Ahern and Clark, we are particularly interested in the growth rates of functions at points of the spectrum of $B$ where $B$ does not admit a derivative in the sense of Carath\\'eodory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1091","kind":"arxiv","version":2},"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":"2026-05-18T02:00:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"npv7RCEiDqiWszSeAfmLZCa6mYZkrvG3VLnnsnhsM9ZM888p54SzUGb1y/UWTn+TvCfC2VstfZg+TlYIZ8WlBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:54:30.823446Z"},"content_sha256":"3357ad7a7fd5360e52457afeb50a7d9804762584d545c8bc7700b727e649bd35","schema_version":"1.0","event_id":"sha256:3357ad7a7fd5360e52457afeb50a7d9804762584d545c8bc7700b727e649bd35"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SBLH32UFVOT7TVKX7OP3OZXLYF/bundle.json","state_url":"https://pith.science/pith/SBLH32UFVOT7TVKX7OP3OZXLYF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SBLH32UFVOT7TVKX7OP3OZXLYF/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":"2026-06-01T12:54:30Z","links":{"resolver":"https://pith.science/pith/SBLH32UFVOT7TVKX7OP3OZXLYF","bundle":"https://pith.science/pith/SBLH32UFVOT7TVKX7OP3OZXLYF/bundle.json","state":"https://pith.science/pith/SBLH32UFVOT7TVKX7OP3OZXLYF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SBLH32UFVOT7TVKX7OP3OZXLYF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SBLH32UFVOT7TVKX7OP3OZXLYF","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":"874796ebc02dca474dc015a84c25d7b0625693b461ef15ef702454a7b316a16f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-09-06T07:14:40Z","title_canon_sha256":"693e2790b029c941813751a8d5f9c82fa7cbf2a483f5007b9997d55f8fbe36ce"},"schema_version":"1.0","source":{"id":"1109.1091","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1091","created_at":"2026-05-18T02:00:39Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1091v2","created_at":"2026-05-18T02:00:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1091","created_at":"2026-05-18T02:00:39Z"},{"alias_kind":"pith_short_12","alias_value":"SBLH32UFVOT7","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SBLH32UFVOT7TVKX","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SBLH32UF","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:3357ad7a7fd5360e52457afeb50a7d9804762584d545c8bc7700b727e649bd35","target":"graph","created_at":"2026-05-18T02:00:39Z","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 discuss the boundary behavior of functions in backward shift invariant subspaces $(B H^2)^{\\perp}$, where $B$ is a Blaschke product. Extending some results of Ahern and Clark, we are particularly interested in the growth rates of functions at points of the spectrum of $B$ where $B$ does not admit a derivative in the sense of Carath\\'eodory.","authors_text":"Andreas Hartmann (IMB), William T. Ross","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-09-06T07:14:40Z","title":"Bad boundary behavior in star invariant subspaces I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1091","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:a63883772716d950035847b97c61654530274ccdbc2d890d50a23281e0f975bc","target":"record","created_at":"2026-05-18T02:00:39Z","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":"874796ebc02dca474dc015a84c25d7b0625693b461ef15ef702454a7b316a16f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-09-06T07:14:40Z","title_canon_sha256":"693e2790b029c941813751a8d5f9c82fa7cbf2a483f5007b9997d55f8fbe36ce"},"schema_version":"1.0","source":{"id":"1109.1091","kind":"arxiv","version":2}},"canonical_sha256":"90567dea85aba7f9d557fb9fb766ebc15bc3844a5f96436de86919bfdccd8c2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90567dea85aba7f9d557fb9fb766ebc15bc3844a5f96436de86919bfdccd8c2e","first_computed_at":"2026-05-18T02:00:39.236272Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:39.236272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HIHjqcrUl/ajytM8IqkqUjTXSPPvwYyM7HB+CzwngyKbRaE1FOSGCideg/fmcVFVt/U1ApuANti8dlZkKxmyCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:39.236926Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.1091","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a63883772716d950035847b97c61654530274ccdbc2d890d50a23281e0f975bc","sha256:3357ad7a7fd5360e52457afeb50a7d9804762584d545c8bc7700b727e649bd35"],"state_sha256":"a72e942a9bd3749e66a6954c601ebfcaeb7a15ef05e15353a68e0b2d671bf31e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5apoHVEe7ePOac6Q1r8voLGG+AxJNTgT9CVCu49z1Sf1MEM8h2kDOuoqbZ1N4zjWeTa4SDpp7ZNYrbEziECJCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:54:30.825493Z","bundle_sha256":"5f9f4ca8d38ca5a8346f41a02f4489ca82ef89bf697d82ff64dfa3f7085d8b02"}}