{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KLB3CSPPXEPSHCDK6HCVD6FKVT","short_pith_number":"pith:KLB3CSPP","canonical_record":{"source":{"id":"1609.04540","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-09-15T08:56:48Z","cross_cats_sorted":[],"title_canon_sha256":"5b6576caf9a31e468d45f4be3d729beec7f7dc1e0d501a3a87fa82662093df0a","abstract_canon_sha256":"d970d20374fce0be4c2598f2ba8a65e73be7bae277b2bbea61a544b3b5e58c10"},"schema_version":"1.0"},"canonical_sha256":"52c3b149efb91f23886af1c551f8aaacda6ad1bc2a6e1ec603aa451d28827e8d","source":{"kind":"arxiv","id":"1609.04540","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04540","created_at":"2026-05-18T00:39:23Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04540v2","created_at":"2026-05-18T00:39:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04540","created_at":"2026-05-18T00:39:23Z"},{"alias_kind":"pith_short_12","alias_value":"KLB3CSPPXEPS","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KLB3CSPPXEPSHCDK","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KLB3CSPP","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KLB3CSPPXEPSHCDK6HCVD6FKVT","target":"record","payload":{"canonical_record":{"source":{"id":"1609.04540","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-09-15T08:56:48Z","cross_cats_sorted":[],"title_canon_sha256":"5b6576caf9a31e468d45f4be3d729beec7f7dc1e0d501a3a87fa82662093df0a","abstract_canon_sha256":"d970d20374fce0be4c2598f2ba8a65e73be7bae277b2bbea61a544b3b5e58c10"},"schema_version":"1.0"},"canonical_sha256":"52c3b149efb91f23886af1c551f8aaacda6ad1bc2a6e1ec603aa451d28827e8d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:23.823130Z","signature_b64":"2lRBNVlhf9ms39d7E5Q1CY8OItk4r1ymr+U+qWI8JBKhxgPeThKtIIFpQ9xb01QsxLlr5ApQV7eX0YNR3EReAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52c3b149efb91f23886af1c551f8aaacda6ad1bc2a6e1ec603aa451d28827e8d","last_reissued_at":"2026-05-18T00:39:23.822272Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:23.822272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.04540","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":"2026-05-18T00:39:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LkjvoR4h/qSfQVYrOiY1dyS9j7+hn/zoDI7pSa8xUCaG4/iucjDcu2FHfsh2qV/GTUD0m5q+mdIU1s0sRMgkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T14:10:30.543240Z"},"content_sha256":"44c84976278b198a888c862794999bddc7180c467e3c65025cd0033e4d0e3add","schema_version":"1.0","event_id":"sha256:44c84976278b198a888c862794999bddc7180c467e3c65025cd0033e4d0e3add"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KLB3CSPPXEPSHCDK6HCVD6FKVT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Around operators not increasing the degree of polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"P. Maroni, T. Augusta Mesquita","submitted_at":"2016-09-15T08:56:48Z","abstract_excerpt":"We present a generic operator $J$ simply defined as a linear map not increasing the degree from the vectorial space of polynomial functions into itself and we address the problem of finding the polynomial sequences that coincide with the (normalized) $J$-image of themselves. The technique developed assembles different types of operators and initiates with a transposition of the problem to the dual space. It is also provided examples where the results are applied to the case where $J$'s expansion is limited to three terms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04540","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":"2026-05-18T00:39:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aa9aCLEyDGXRTkyJ/o4nj8GDcGqrlBkgUa975kirnX38KAENb1SMTUbShzszFZpBNAVUgAdjv2Ijl44eV4ZrBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T14:10:30.543600Z"},"content_sha256":"5c31c5a61179406cc761447464bbe7b1f689ab1695312f56de42b8d5b2e32ae1","schema_version":"1.0","event_id":"sha256:5c31c5a61179406cc761447464bbe7b1f689ab1695312f56de42b8d5b2e32ae1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KLB3CSPPXEPSHCDK6HCVD6FKVT/bundle.json","state_url":"https://pith.science/pith/KLB3CSPPXEPSHCDK6HCVD6FKVT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KLB3CSPPXEPSHCDK6HCVD6FKVT/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":"2026-07-02T14:10:30Z","links":{"resolver":"https://pith.science/pith/KLB3CSPPXEPSHCDK6HCVD6FKVT","bundle":"https://pith.science/pith/KLB3CSPPXEPSHCDK6HCVD6FKVT/bundle.json","state":"https://pith.science/pith/KLB3CSPPXEPSHCDK6HCVD6FKVT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KLB3CSPPXEPSHCDK6HCVD6FKVT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KLB3CSPPXEPSHCDK6HCVD6FKVT","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":"d970d20374fce0be4c2598f2ba8a65e73be7bae277b2bbea61a544b3b5e58c10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-09-15T08:56:48Z","title_canon_sha256":"5b6576caf9a31e468d45f4be3d729beec7f7dc1e0d501a3a87fa82662093df0a"},"schema_version":"1.0","source":{"id":"1609.04540","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04540","created_at":"2026-05-18T00:39:23Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04540v2","created_at":"2026-05-18T00:39:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04540","created_at":"2026-05-18T00:39:23Z"},{"alias_kind":"pith_short_12","alias_value":"KLB3CSPPXEPS","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KLB3CSPPXEPSHCDK","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KLB3CSPP","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:5c31c5a61179406cc761447464bbe7b1f689ab1695312f56de42b8d5b2e32ae1","target":"graph","created_at":"2026-05-18T00:39:23Z","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 present a generic operator $J$ simply defined as a linear map not increasing the degree from the vectorial space of polynomial functions into itself and we address the problem of finding the polynomial sequences that coincide with the (normalized) $J$-image of themselves. The technique developed assembles different types of operators and initiates with a transposition of the problem to the dual space. It is also provided examples where the results are applied to the case where $J$'s expansion is limited to three terms.","authors_text":"P. Maroni, T. Augusta Mesquita","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-09-15T08:56:48Z","title":"Around operators not increasing the degree of polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04540","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":"sha256:44c84976278b198a888c862794999bddc7180c467e3c65025cd0033e4d0e3add","target":"record","created_at":"2026-05-18T00:39:23Z","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":"d970d20374fce0be4c2598f2ba8a65e73be7bae277b2bbea61a544b3b5e58c10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-09-15T08:56:48Z","title_canon_sha256":"5b6576caf9a31e468d45f4be3d729beec7f7dc1e0d501a3a87fa82662093df0a"},"schema_version":"1.0","source":{"id":"1609.04540","kind":"arxiv","version":2}},"canonical_sha256":"52c3b149efb91f23886af1c551f8aaacda6ad1bc2a6e1ec603aa451d28827e8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52c3b149efb91f23886af1c551f8aaacda6ad1bc2a6e1ec603aa451d28827e8d","first_computed_at":"2026-05-18T00:39:23.822272Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:23.822272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2lRBNVlhf9ms39d7E5Q1CY8OItk4r1ymr+U+qWI8JBKhxgPeThKtIIFpQ9xb01QsxLlr5ApQV7eX0YNR3EReAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:23.823130Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.04540","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44c84976278b198a888c862794999bddc7180c467e3c65025cd0033e4d0e3add","sha256:5c31c5a61179406cc761447464bbe7b1f689ab1695312f56de42b8d5b2e32ae1"],"state_sha256":"679a54239977cf7daa300df390c49d2ad6c873546af03d004eb080b6ce548848"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TfQPkkGhRm1rtATIwq8KBiESUAHOCWO5KJYUXL/Q0/qloadw7pEvdMuvkioq8BalK2F7lUlS7w42drR8o4MmAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T14:10:30.545508Z","bundle_sha256":"31e8d0d4c9916c37857f99962b7e5b8839c9db0b5c1b2053c703a2d410306644"}}