{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:4ZCSKVMBE4DB5K64XQDZHBRGVK","short_pith_number":"pith:4ZCSKVMB","canonical_record":{"source":{"id":"2605.30114","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2026-05-28T15:50:08Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"766bf1e57ea20ac049c339702ae7342c99a31c501111bb1229ec7382cbccb410","abstract_canon_sha256":"fe14180c8a2cdbeb084549c62e93d0e6938ae5616e1a56936bf56217d027ba01"},"schema_version":"1.0"},"canonical_sha256":"e64525558127061eabdcbc07938626aaa6f025de376d515fdc7f5812f5d19fa5","source":{"kind":"arxiv","id":"2605.30114","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.30114","created_at":"2026-05-29T02:06:10Z"},{"alias_kind":"arxiv_version","alias_value":"2605.30114v1","created_at":"2026-05-29T02:06:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.30114","created_at":"2026-05-29T02:06:10Z"},{"alias_kind":"pith_short_12","alias_value":"4ZCSKVMBE4DB","created_at":"2026-05-29T02:06:10Z"},{"alias_kind":"pith_short_16","alias_value":"4ZCSKVMBE4DB5K64","created_at":"2026-05-29T02:06:10Z"},{"alias_kind":"pith_short_8","alias_value":"4ZCSKVMB","created_at":"2026-05-29T02:06:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:4ZCSKVMBE4DB5K64XQDZHBRGVK","target":"record","payload":{"canonical_record":{"source":{"id":"2605.30114","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2026-05-28T15:50:08Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"766bf1e57ea20ac049c339702ae7342c99a31c501111bb1229ec7382cbccb410","abstract_canon_sha256":"fe14180c8a2cdbeb084549c62e93d0e6938ae5616e1a56936bf56217d027ba01"},"schema_version":"1.0"},"canonical_sha256":"e64525558127061eabdcbc07938626aaa6f025de376d515fdc7f5812f5d19fa5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T02:06:10.146037Z","signature_b64":"N3uSXYGyIdSuPeJogPt5FXkYlr+QJqwc1nx6nRqC828dH/tWpkDwIQZgssBajxVc0HrE2RoKxpppoxFhCWbcAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e64525558127061eabdcbc07938626aaa6f025de376d515fdc7f5812f5d19fa5","last_reissued_at":"2026-05-29T02:06:10.145697Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T02:06:10.145697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.30114","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":"2026-05-29T02:06:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R8XrhnztrptAYITiru3uNxf3dg3988eY5D9XQ7kMfZJWB+00O3nxKxJzwC70JJsMmXFZwt2C3lZDUbKtDjwgAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:30:21.960815Z"},"content_sha256":"102e5b5b5302930fa3ae4402a185b13268742cced031e9c6e4c37ff7bf343423","schema_version":"1.0","event_id":"sha256:102e5b5b5302930fa3ae4402a185b13268742cced031e9c6e4c37ff7bf343423"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:4ZCSKVMBE4DB5K64XQDZHBRGVK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the coefficient formula for de Branges-Rovnyak norms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Thomas Ransford","submitted_at":"2026-05-28T15:50:08Z","abstract_excerpt":"Let $\\mathcal{H}(b)$ be the de Branges-Rovnyak space associated to a non-extreme point $b$ of the unit ball of $H^\\infty$, and let $\\phi=b/a$, where $a$ is the Pythagorean mate of $b$. It is known that, if $f$ is a function holomorphic on a neighbourhood of the closed unit disk, then it belongs to $\\mathcal{H}(b)$, and its norm in $\\mathcal{H}(b)$ can be expressed in terms of the Taylor coefficients of $f$ and $\\phi$ via the formula \\[ \\|f\\|_{\\mathcal{H}(b)}^2=\\sum_{m\\ge0}|\\hat{f}(m)|^2 +\\sum_{m\\ge0}\\Bigl|\\sum_{n\\ge0}\\overline{\\hat{\\phi}(n)}\\hat{f}(m+n)\\Bigr|^2. \\] However, the formula can bre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30114","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.30114/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-29T02:06:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ccNYA5ucHFnZR1vlc8/xZWSnpqVBUDPXyM+4gZpT8AlAETaMyxpF+AKfoHTTsy2k4eGsmaoAywcwlcPolok4Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:30:21.961200Z"},"content_sha256":"11485cbd589380fc47ca67b20b3db168400ff70b8a45d1758f4357a265f15027","schema_version":"1.0","event_id":"sha256:11485cbd589380fc47ca67b20b3db168400ff70b8a45d1758f4357a265f15027"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4ZCSKVMBE4DB5K64XQDZHBRGVK/bundle.json","state_url":"https://pith.science/pith/4ZCSKVMBE4DB5K64XQDZHBRGVK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4ZCSKVMBE4DB5K64XQDZHBRGVK/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":"2026-06-23T17:30:21Z","links":{"resolver":"https://pith.science/pith/4ZCSKVMBE4DB5K64XQDZHBRGVK","bundle":"https://pith.science/pith/4ZCSKVMBE4DB5K64XQDZHBRGVK/bundle.json","state":"https://pith.science/pith/4ZCSKVMBE4DB5K64XQDZHBRGVK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4ZCSKVMBE4DB5K64XQDZHBRGVK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:4ZCSKVMBE4DB5K64XQDZHBRGVK","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":"fe14180c8a2cdbeb084549c62e93d0e6938ae5616e1a56936bf56217d027ba01","cross_cats_sorted":["math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2026-05-28T15:50:08Z","title_canon_sha256":"766bf1e57ea20ac049c339702ae7342c99a31c501111bb1229ec7382cbccb410"},"schema_version":"1.0","source":{"id":"2605.30114","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.30114","created_at":"2026-05-29T02:06:10Z"},{"alias_kind":"arxiv_version","alias_value":"2605.30114v1","created_at":"2026-05-29T02:06:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.30114","created_at":"2026-05-29T02:06:10Z"},{"alias_kind":"pith_short_12","alias_value":"4ZCSKVMBE4DB","created_at":"2026-05-29T02:06:10Z"},{"alias_kind":"pith_short_16","alias_value":"4ZCSKVMBE4DB5K64","created_at":"2026-05-29T02:06:10Z"},{"alias_kind":"pith_short_8","alias_value":"4ZCSKVMB","created_at":"2026-05-29T02:06:10Z"}],"graph_snapshots":[{"event_id":"sha256:11485cbd589380fc47ca67b20b3db168400ff70b8a45d1758f4357a265f15027","target":"graph","created_at":"2026-05-29T02:06:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.30114/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathcal{H}(b)$ be the de Branges-Rovnyak space associated to a non-extreme point $b$ of the unit ball of $H^\\infty$, and let $\\phi=b/a$, where $a$ is the Pythagorean mate of $b$. It is known that, if $f$ is a function holomorphic on a neighbourhood of the closed unit disk, then it belongs to $\\mathcal{H}(b)$, and its norm in $\\mathcal{H}(b)$ can be expressed in terms of the Taylor coefficients of $f$ and $\\phi$ via the formula \\[ \\|f\\|_{\\mathcal{H}(b)}^2=\\sum_{m\\ge0}|\\hat{f}(m)|^2 +\\sum_{m\\ge0}\\Bigl|\\sum_{n\\ge0}\\overline{\\hat{\\phi}(n)}\\hat{f}(m+n)\\Bigr|^2. \\] However, the formula can bre","authors_text":"Thomas Ransford","cross_cats":["math.FA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2026-05-28T15:50:08Z","title":"On the coefficient formula for de Branges-Rovnyak norms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30114","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":"sha256:102e5b5b5302930fa3ae4402a185b13268742cced031e9c6e4c37ff7bf343423","target":"record","created_at":"2026-05-29T02:06:10Z","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":"fe14180c8a2cdbeb084549c62e93d0e6938ae5616e1a56936bf56217d027ba01","cross_cats_sorted":["math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2026-05-28T15:50:08Z","title_canon_sha256":"766bf1e57ea20ac049c339702ae7342c99a31c501111bb1229ec7382cbccb410"},"schema_version":"1.0","source":{"id":"2605.30114","kind":"arxiv","version":1}},"canonical_sha256":"e64525558127061eabdcbc07938626aaa6f025de376d515fdc7f5812f5d19fa5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e64525558127061eabdcbc07938626aaa6f025de376d515fdc7f5812f5d19fa5","first_computed_at":"2026-05-29T02:06:10.145697Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T02:06:10.145697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N3uSXYGyIdSuPeJogPt5FXkYlr+QJqwc1nx6nRqC828dH/tWpkDwIQZgssBajxVc0HrE2RoKxpppoxFhCWbcAA==","signature_status":"signed_v1","signed_at":"2026-05-29T02:06:10.146037Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.30114","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:102e5b5b5302930fa3ae4402a185b13268742cced031e9c6e4c37ff7bf343423","sha256:11485cbd589380fc47ca67b20b3db168400ff70b8a45d1758f4357a265f15027"],"state_sha256":"a2928116e792eab1fb1f0545c350b4b0b88ef0a180b8ca956861891fc5109d3f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7vXRzaYhGZ4UEVnIcg7ddwjL9Te4He6RkmODBHnz8DQgs3NkU1w4keLEG6BXYVD+2/ivePSFHE+Q2xJGjTZcCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T17:30:21.963457Z","bundle_sha256":"52787df2a08593ba93cf0099eddcd3e4f93819213dbd763c0d872bdce3de1545"}}