{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:UZCN2Z3JO7BGWH3C3DXZDF7UK2","short_pith_number":"pith:UZCN2Z3J","canonical_record":{"source":{"id":"1702.00765","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-02-02T17:53:34Z","cross_cats_sorted":[],"title_canon_sha256":"5d6aca86ab26db48cf1b5b4c5a7165ff5dd70ed3668a5d4c0ed0d964c6d6095e","abstract_canon_sha256":"40f4701e79b1944e7112980d6fe5763c3774567967a777e2a73c8671f9aa1877"},"schema_version":"1.0"},"canonical_sha256":"a644dd676977c26b1f62d8ef9197f456a08e900238d8fcdbbcf95b46f0ffe54e","source":{"kind":"arxiv","id":"1702.00765","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.00765","created_at":"2026-05-18T00:51:30Z"},{"alias_kind":"arxiv_version","alias_value":"1702.00765v1","created_at":"2026-05-18T00:51:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.00765","created_at":"2026-05-18T00:51:30Z"},{"alias_kind":"pith_short_12","alias_value":"UZCN2Z3JO7BG","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UZCN2Z3JO7BGWH3C","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UZCN2Z3J","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:UZCN2Z3JO7BGWH3C3DXZDF7UK2","target":"record","payload":{"canonical_record":{"source":{"id":"1702.00765","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-02-02T17:53:34Z","cross_cats_sorted":[],"title_canon_sha256":"5d6aca86ab26db48cf1b5b4c5a7165ff5dd70ed3668a5d4c0ed0d964c6d6095e","abstract_canon_sha256":"40f4701e79b1944e7112980d6fe5763c3774567967a777e2a73c8671f9aa1877"},"schema_version":"1.0"},"canonical_sha256":"a644dd676977c26b1f62d8ef9197f456a08e900238d8fcdbbcf95b46f0ffe54e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:30.897355Z","signature_b64":"3sNcAAQXvnokglLZT0UwHbt6lB/XE6ZMDvN2Uji6SAbLAZziaMCnMBGpJ+lip8/jYR7wzm5TF7GJYW1kiccdAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a644dd676977c26b1f62d8ef9197f456a08e900238d8fcdbbcf95b46f0ffe54e","last_reissued_at":"2026-05-18T00:51:30.896670Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:30.896670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.00765","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":"2026-05-18T00:51:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rIVLHKYGB+p9PBTC2/xuXKiJqXw2/mrt9GgOcE1GyUCjaJU0gHd1meryZbZ/3DS1qlNMMCxa61i48+TsTSbQAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T04:59:56.606907Z"},"content_sha256":"0c5c02671ade3dc89754529a1fc6ef30d7ff44e417b8da0101d75496027b4f04","schema_version":"1.0","event_id":"sha256:0c5c02671ade3dc89754529a1fc6ef30d7ff44e417b8da0101d75496027b4f04"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:UZCN2Z3JO7BGWH3C3DXZDF7UK2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weighted shifts on directed trees. Their multiplier algebras, reflexivity and decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Artur Planeta, Marek Ptak, Piotr Budzynski, Piotr Dymek","submitted_at":"2017-02-02T17:53:34Z","abstract_excerpt":"We study bounded weighted shifts on directed trees. We show that the set of multiplication operators associated with an injective weighted shift on a rooted directed tree coincides with the WOT/SOT closure of the set of polynomials of the weighted shift. From this fact we deduce reflexivity of those weighted shifts on rooted directed trees whose all path-induced spectral-like radii are positive. We show that weighted shifts with positive weights on rooted directed trees admit a Wold-type decomposition. We prove that the pairwise orthogonality of the factors in the decomposition is equivalent t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00765","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":"2026-05-18T00:51:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pgHTWgdBMXvlelTFTUe472NDEG4CQZaKgjq6YYetFsdeCTgG8ihOQ9taYZb6eWkC1DJWmPWnKgSeNh/4x7gOBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T04:59:56.607508Z"},"content_sha256":"95858adc5c40d7c53f0abebeb0ad4eb51a50215526dc5c5533ed6e662aeb2a87","schema_version":"1.0","event_id":"sha256:95858adc5c40d7c53f0abebeb0ad4eb51a50215526dc5c5533ed6e662aeb2a87"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UZCN2Z3JO7BGWH3C3DXZDF7UK2/bundle.json","state_url":"https://pith.science/pith/UZCN2Z3JO7BGWH3C3DXZDF7UK2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UZCN2Z3JO7BGWH3C3DXZDF7UK2/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":"2026-06-11T04:59:56Z","links":{"resolver":"https://pith.science/pith/UZCN2Z3JO7BGWH3C3DXZDF7UK2","bundle":"https://pith.science/pith/UZCN2Z3JO7BGWH3C3DXZDF7UK2/bundle.json","state":"https://pith.science/pith/UZCN2Z3JO7BGWH3C3DXZDF7UK2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UZCN2Z3JO7BGWH3C3DXZDF7UK2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UZCN2Z3JO7BGWH3C3DXZDF7UK2","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":"40f4701e79b1944e7112980d6fe5763c3774567967a777e2a73c8671f9aa1877","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-02-02T17:53:34Z","title_canon_sha256":"5d6aca86ab26db48cf1b5b4c5a7165ff5dd70ed3668a5d4c0ed0d964c6d6095e"},"schema_version":"1.0","source":{"id":"1702.00765","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.00765","created_at":"2026-05-18T00:51:30Z"},{"alias_kind":"arxiv_version","alias_value":"1702.00765v1","created_at":"2026-05-18T00:51:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.00765","created_at":"2026-05-18T00:51:30Z"},{"alias_kind":"pith_short_12","alias_value":"UZCN2Z3JO7BG","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UZCN2Z3JO7BGWH3C","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UZCN2Z3J","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:95858adc5c40d7c53f0abebeb0ad4eb51a50215526dc5c5533ed6e662aeb2a87","target":"graph","created_at":"2026-05-18T00:51:30Z","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 study bounded weighted shifts on directed trees. We show that the set of multiplication operators associated with an injective weighted shift on a rooted directed tree coincides with the WOT/SOT closure of the set of polynomials of the weighted shift. From this fact we deduce reflexivity of those weighted shifts on rooted directed trees whose all path-induced spectral-like radii are positive. We show that weighted shifts with positive weights on rooted directed trees admit a Wold-type decomposition. We prove that the pairwise orthogonality of the factors in the decomposition is equivalent t","authors_text":"Artur Planeta, Marek Ptak, Piotr Budzynski, Piotr Dymek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-02-02T17:53:34Z","title":"Weighted shifts on directed trees. Their multiplier algebras, reflexivity and decompositions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00765","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":"sha256:0c5c02671ade3dc89754529a1fc6ef30d7ff44e417b8da0101d75496027b4f04","target":"record","created_at":"2026-05-18T00:51:30Z","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":"40f4701e79b1944e7112980d6fe5763c3774567967a777e2a73c8671f9aa1877","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-02-02T17:53:34Z","title_canon_sha256":"5d6aca86ab26db48cf1b5b4c5a7165ff5dd70ed3668a5d4c0ed0d964c6d6095e"},"schema_version":"1.0","source":{"id":"1702.00765","kind":"arxiv","version":1}},"canonical_sha256":"a644dd676977c26b1f62d8ef9197f456a08e900238d8fcdbbcf95b46f0ffe54e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a644dd676977c26b1f62d8ef9197f456a08e900238d8fcdbbcf95b46f0ffe54e","first_computed_at":"2026-05-18T00:51:30.896670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:30.896670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3sNcAAQXvnokglLZT0UwHbt6lB/XE6ZMDvN2Uji6SAbLAZziaMCnMBGpJ+lip8/jYR7wzm5TF7GJYW1kiccdAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:30.897355Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.00765","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c5c02671ade3dc89754529a1fc6ef30d7ff44e417b8da0101d75496027b4f04","sha256:95858adc5c40d7c53f0abebeb0ad4eb51a50215526dc5c5533ed6e662aeb2a87"],"state_sha256":"c2d93a2f993d1e05ee36cc96b771b9c08094ce6e852cfef356e52f5e9063afc9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uVJi8wC+kGrk2Fi1ZcH8bXb+Cbg8SpABt1qcPasFB5eAnpH2w8dFHeJpEerH3PxeQgxP7C/R93MnVdmbNVqTBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T04:59:56.610969Z","bundle_sha256":"f4dcb1c3bd3f1901e2774eab37c68a8cc41819b31ff4831f2fca9bc588ed1d07"}}