{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:S7WSDQBZTHHMAEYEE4CNUQAPKK","short_pith_number":"pith:S7WSDQBZ","canonical_record":{"source":{"id":"2606.22912","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-06-22T06:53:36Z","cross_cats_sorted":[],"title_canon_sha256":"35633482e8ac6af8d62e0223e7d5d93bea87896fbc03a10018df261b0f58f5fc","abstract_canon_sha256":"4bc7e1b397bfdc477a2a71e2aafe7204ab55d70a761f1da1f0c0bc93dbfca153"},"schema_version":"1.0"},"canonical_sha256":"97ed21c03999cec013042704da400f5281526b1314cd2ca4a9bf50e15cfeccf5","source":{"kind":"arxiv","id":"2606.22912","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22912","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22912v1","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22912","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"pith_short_12","alias_value":"S7WSDQBZTHHM","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"pith_short_16","alias_value":"S7WSDQBZTHHMAEYE","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"pith_short_8","alias_value":"S7WSDQBZ","created_at":"2026-06-23T03:14:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:S7WSDQBZTHHMAEYEE4CNUQAPKK","target":"record","payload":{"canonical_record":{"source":{"id":"2606.22912","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-06-22T06:53:36Z","cross_cats_sorted":[],"title_canon_sha256":"35633482e8ac6af8d62e0223e7d5d93bea87896fbc03a10018df261b0f58f5fc","abstract_canon_sha256":"4bc7e1b397bfdc477a2a71e2aafe7204ab55d70a761f1da1f0c0bc93dbfca153"},"schema_version":"1.0"},"canonical_sha256":"97ed21c03999cec013042704da400f5281526b1314cd2ca4a9bf50e15cfeccf5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T03:14:03.992893Z","signature_b64":"+l88lEPwGRJhMRw8UvB7axyDDf2+qBB0YOnLsYkhDpm1/wmCMz99Y8EPrcd40ZpnMYHN7pxB1yYWQF81YqFyCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97ed21c03999cec013042704da400f5281526b1314cd2ca4a9bf50e15cfeccf5","last_reissued_at":"2026-06-23T03:14:03.992389Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T03:14:03.992389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.22912","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":"2026-06-23T03:14:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"83GYEYpmEo+XsZNZM+Iw8e2+osX91KjRgiRleT0cAZtvx8fZo4nGRNwYf+Ak1EgvPWBR/o/g2gNOSzipH5WzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:54:59.138038Z"},"content_sha256":"f307d5894b5b89e128016ac21e01b4b6cc02eac77c85e411d0a9a5bb63004d35","schema_version":"1.0","event_id":"sha256:f307d5894b5b89e128016ac21e01b4b6cc02eac77c85e411d0a9a5bb63004d35"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:S7WSDQBZTHHMAEYEE4CNUQAPKK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convolution Operators on Weighted Hahn Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Arnab Patra, Sayan Saha","submitted_at":"2026-06-22T06:53:36Z","abstract_excerpt":"This paper studies the convolution operator on weighted Hahn sequence spaces. The boundedness and compactness of these operators, together with the multiplier algebras of the weighted Hahn space and its dual, are investigated. A complete characterization of the spectrum and fine spectrum is obtained, with illustrative examples. The introduction of the weighted framework leads to the emergence of new multiplier and spectral properties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22912","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/2606.22912/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":"2026-06-23T03:14:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IT12s+tCrfPQXcOiMgmhpgAa9oRzZ94ChBnw1UZ/vmq5czvkdjv5Je/D/ySCakC7c1JWXVFixPo7thiG5xFWBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:54:59.138402Z"},"content_sha256":"ac17646f3ac61949baa17e966764208688793a4dc2bb00fb1fc1c16a8c8bc4ff","schema_version":"1.0","event_id":"sha256:ac17646f3ac61949baa17e966764208688793a4dc2bb00fb1fc1c16a8c8bc4ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S7WSDQBZTHHMAEYEE4CNUQAPKK/bundle.json","state_url":"https://pith.science/pith/S7WSDQBZTHHMAEYEE4CNUQAPKK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S7WSDQBZTHHMAEYEE4CNUQAPKK/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":"2026-06-27T02:54:59Z","links":{"resolver":"https://pith.science/pith/S7WSDQBZTHHMAEYEE4CNUQAPKK","bundle":"https://pith.science/pith/S7WSDQBZTHHMAEYEE4CNUQAPKK/bundle.json","state":"https://pith.science/pith/S7WSDQBZTHHMAEYEE4CNUQAPKK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S7WSDQBZTHHMAEYEE4CNUQAPKK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:S7WSDQBZTHHMAEYEE4CNUQAPKK","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":"4bc7e1b397bfdc477a2a71e2aafe7204ab55d70a761f1da1f0c0bc93dbfca153","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-06-22T06:53:36Z","title_canon_sha256":"35633482e8ac6af8d62e0223e7d5d93bea87896fbc03a10018df261b0f58f5fc"},"schema_version":"1.0","source":{"id":"2606.22912","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22912","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22912v1","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22912","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"pith_short_12","alias_value":"S7WSDQBZTHHM","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"pith_short_16","alias_value":"S7WSDQBZTHHMAEYE","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"pith_short_8","alias_value":"S7WSDQBZ","created_at":"2026-06-23T03:14:03Z"}],"graph_snapshots":[{"event_id":"sha256:ac17646f3ac61949baa17e966764208688793a4dc2bb00fb1fc1c16a8c8bc4ff","target":"graph","created_at":"2026-06-23T03:14:03Z","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/2606.22912/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies the convolution operator on weighted Hahn sequence spaces. The boundedness and compactness of these operators, together with the multiplier algebras of the weighted Hahn space and its dual, are investigated. A complete characterization of the spectrum and fine spectrum is obtained, with illustrative examples. The introduction of the weighted framework leads to the emergence of new multiplier and spectral properties.","authors_text":"Arnab Patra, Sayan Saha","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-06-22T06:53:36Z","title":"Convolution Operators on Weighted Hahn Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22912","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:f307d5894b5b89e128016ac21e01b4b6cc02eac77c85e411d0a9a5bb63004d35","target":"record","created_at":"2026-06-23T03:14:03Z","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":"4bc7e1b397bfdc477a2a71e2aafe7204ab55d70a761f1da1f0c0bc93dbfca153","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-06-22T06:53:36Z","title_canon_sha256":"35633482e8ac6af8d62e0223e7d5d93bea87896fbc03a10018df261b0f58f5fc"},"schema_version":"1.0","source":{"id":"2606.22912","kind":"arxiv","version":1}},"canonical_sha256":"97ed21c03999cec013042704da400f5281526b1314cd2ca4a9bf50e15cfeccf5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97ed21c03999cec013042704da400f5281526b1314cd2ca4a9bf50e15cfeccf5","first_computed_at":"2026-06-23T03:14:03.992389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T03:14:03.992389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+l88lEPwGRJhMRw8UvB7axyDDf2+qBB0YOnLsYkhDpm1/wmCMz99Y8EPrcd40ZpnMYHN7pxB1yYWQF81YqFyCQ==","signature_status":"signed_v1","signed_at":"2026-06-23T03:14:03.992893Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.22912","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f307d5894b5b89e128016ac21e01b4b6cc02eac77c85e411d0a9a5bb63004d35","sha256:ac17646f3ac61949baa17e966764208688793a4dc2bb00fb1fc1c16a8c8bc4ff"],"state_sha256":"6e4ec60e06901c2454ed68293a524eb0b0964b65373650edf63e255b9a0af87a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OLEozY5AeTf575g+KRbH9Qs3vgy4TDnCn94gYIYMZkWapC7xI1lwYzr3CzOYWLLy390e2wWJ3erP2JultsaIBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T02:54:59.140204Z","bundle_sha256":"b15156d776b466c9ab991b5787aa4c838705f802c992f41a990fde56c4af2209"}}