{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:MKIMOW6BCPJX5B5FXMVBV3EGAP","short_pith_number":"pith:MKIMOW6B","canonical_record":{"source":{"id":"2206.14419","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2022-06-29T06:28:00Z","cross_cats_sorted":[],"title_canon_sha256":"e7a79839619c4c7843789f837f027bba05c987439ac32754d63e8d287842b8a9","abstract_canon_sha256":"06d957afd91c3e8705e8246e3f19bdb63e391078c06e39c0cb2dda7d933871dd"},"schema_version":"1.0"},"canonical_sha256":"6290c75bc113d37e87a5bb2a1aec8603c8fdab50ecae9b7454cce8c282c99624","source":{"kind":"arxiv","id":"2206.14419","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.14419","created_at":"2026-07-05T04:36:04Z"},{"alias_kind":"arxiv_version","alias_value":"2206.14419v1","created_at":"2026-07-05T04:36:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.14419","created_at":"2026-07-05T04:36:04Z"},{"alias_kind":"pith_short_12","alias_value":"MKIMOW6BCPJX","created_at":"2026-07-05T04:36:04Z"},{"alias_kind":"pith_short_16","alias_value":"MKIMOW6BCPJX5B5F","created_at":"2026-07-05T04:36:04Z"},{"alias_kind":"pith_short_8","alias_value":"MKIMOW6B","created_at":"2026-07-05T04:36:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:MKIMOW6BCPJX5B5FXMVBV3EGAP","target":"record","payload":{"canonical_record":{"source":{"id":"2206.14419","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2022-06-29T06:28:00Z","cross_cats_sorted":[],"title_canon_sha256":"e7a79839619c4c7843789f837f027bba05c987439ac32754d63e8d287842b8a9","abstract_canon_sha256":"06d957afd91c3e8705e8246e3f19bdb63e391078c06e39c0cb2dda7d933871dd"},"schema_version":"1.0"},"canonical_sha256":"6290c75bc113d37e87a5bb2a1aec8603c8fdab50ecae9b7454cce8c282c99624","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:36:04.043082Z","signature_b64":"n0leY5rdoCVdmEnkTlOL44LwMwPb8ideJaVDnpQ5MIuj9/SAteDirT/6h4eMZJVF67i/w26lw5i30ZMJyvtkBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6290c75bc113d37e87a5bb2a1aec8603c8fdab50ecae9b7454cce8c282c99624","last_reissued_at":"2026-07-05T04:36:04.042603Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:36:04.042603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2206.14419","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":"2026-07-05T04:36:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"juROk63s8A20KVSIsoo1avB504l2hfpRWOu24EIWsndfoU0T8NXevzwOn2mazocbGw1jGC2j2C1EsfapmRSSAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T11:48:15.918813Z"},"content_sha256":"c502d49d6bbf639293ea73272f806ab563cc83fcc09c170012c23ddda354f67d","schema_version":"1.0","event_id":"sha256:c502d49d6bbf639293ea73272f806ab563cc83fcc09c170012c23ddda354f67d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:MKIMOW6BCPJX5B5FXMVBV3EGAP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractal polynomials On the Sierpi\\'nski gasket and some dimensional results","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"S. Verma, T. Som, V. Agrawal","submitted_at":"2022-06-29T06:28:00Z","abstract_excerpt":"In this paper, we explore some significant properties associated with a fractal operator on the space of all continuous functions defined on the Sierpi\\'nski Gasket (SG). We also provide some results related to constrained approximation with fractal polynomials and study the best approximation properties of fractal polynomials defined on the SG. Further we discuss some remarks on the class of polynomials defined on the SG and try to estimate the fractal dimensions of the graph of $\\alpha$- fractal function defined on the SG by using the oscillation of functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.14419","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/2206.14419/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":"2026-07-05T04:36:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NAs3u4kY5dfg4e/lgSpZ0fEOniyvmn+Vrh2FoADCEkcwZ1LRo2i9QutR1k83WyO7msBIsR5EGwmytLTqCaCjAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T11:48:15.919325Z"},"content_sha256":"56dfa3fbbade62eb859fbb213a629ffa6ac27d1cc7b395c0c26def874936ca11","schema_version":"1.0","event_id":"sha256:56dfa3fbbade62eb859fbb213a629ffa6ac27d1cc7b395c0c26def874936ca11"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MKIMOW6BCPJX5B5FXMVBV3EGAP/bundle.json","state_url":"https://pith.science/pith/MKIMOW6BCPJX5B5FXMVBV3EGAP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MKIMOW6BCPJX5B5FXMVBV3EGAP/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":"2026-08-04T11:48:15Z","links":{"resolver":"https://pith.science/pith/MKIMOW6BCPJX5B5FXMVBV3EGAP","bundle":"https://pith.science/pith/MKIMOW6BCPJX5B5FXMVBV3EGAP/bundle.json","state":"https://pith.science/pith/MKIMOW6BCPJX5B5FXMVBV3EGAP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MKIMOW6BCPJX5B5FXMVBV3EGAP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:MKIMOW6BCPJX5B5FXMVBV3EGAP","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":"06d957afd91c3e8705e8246e3f19bdb63e391078c06e39c0cb2dda7d933871dd","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2022-06-29T06:28:00Z","title_canon_sha256":"e7a79839619c4c7843789f837f027bba05c987439ac32754d63e8d287842b8a9"},"schema_version":"1.0","source":{"id":"2206.14419","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.14419","created_at":"2026-07-05T04:36:04Z"},{"alias_kind":"arxiv_version","alias_value":"2206.14419v1","created_at":"2026-07-05T04:36:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.14419","created_at":"2026-07-05T04:36:04Z"},{"alias_kind":"pith_short_12","alias_value":"MKIMOW6BCPJX","created_at":"2026-07-05T04:36:04Z"},{"alias_kind":"pith_short_16","alias_value":"MKIMOW6BCPJX5B5F","created_at":"2026-07-05T04:36:04Z"},{"alias_kind":"pith_short_8","alias_value":"MKIMOW6B","created_at":"2026-07-05T04:36:04Z"}],"graph_snapshots":[{"event_id":"sha256:56dfa3fbbade62eb859fbb213a629ffa6ac27d1cc7b395c0c26def874936ca11","target":"graph","created_at":"2026-07-05T04:36:04Z","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/2206.14419/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we explore some significant properties associated with a fractal operator on the space of all continuous functions defined on the Sierpi\\'nski Gasket (SG). We also provide some results related to constrained approximation with fractal polynomials and study the best approximation properties of fractal polynomials defined on the SG. Further we discuss some remarks on the class of polynomials defined on the SG and try to estimate the fractal dimensions of the graph of $\\alpha$- fractal function defined on the SG by using the oscillation of functions.","authors_text":"S. Verma, T. Som, V. Agrawal","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2022-06-29T06:28:00Z","title":"Fractal polynomials On the Sierpi\\'nski gasket and some dimensional results"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.14419","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:c502d49d6bbf639293ea73272f806ab563cc83fcc09c170012c23ddda354f67d","target":"record","created_at":"2026-07-05T04:36:04Z","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":"06d957afd91c3e8705e8246e3f19bdb63e391078c06e39c0cb2dda7d933871dd","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2022-06-29T06:28:00Z","title_canon_sha256":"e7a79839619c4c7843789f837f027bba05c987439ac32754d63e8d287842b8a9"},"schema_version":"1.0","source":{"id":"2206.14419","kind":"arxiv","version":1}},"canonical_sha256":"6290c75bc113d37e87a5bb2a1aec8603c8fdab50ecae9b7454cce8c282c99624","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6290c75bc113d37e87a5bb2a1aec8603c8fdab50ecae9b7454cce8c282c99624","first_computed_at":"2026-07-05T04:36:04.042603Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:36:04.042603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n0leY5rdoCVdmEnkTlOL44LwMwPb8ideJaVDnpQ5MIuj9/SAteDirT/6h4eMZJVF67i/w26lw5i30ZMJyvtkBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:36:04.043082Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.14419","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c502d49d6bbf639293ea73272f806ab563cc83fcc09c170012c23ddda354f67d","sha256:56dfa3fbbade62eb859fbb213a629ffa6ac27d1cc7b395c0c26def874936ca11"],"state_sha256":"fbd18e0ccc496c0d6758fef58401b36b4809003b31dd8930a84ab7ca27b504ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sJOVxkLtz8ksZWE1XdUm8lWdsPh0NXffqXy80/L4JXMoB6uV2GncJjkLs5jM7QDvsX4Cai6fcWHr3ENG/WJZBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T11:48:15.925273Z","bundle_sha256":"0d395b84faa4561ebdbd7ec8dd600e6d0c5db26d9ad86179abd2ae1c7b550d00"}}