{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:63TRE5GA3NPQY644URDZ6NQEJI","short_pith_number":"pith:63TRE5GA","canonical_record":{"source":{"id":"1908.03604","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-09T19:25:23Z","cross_cats_sorted":[],"title_canon_sha256":"200d3699518696becb79894cab6934fea00486ffae81d58d0b751d30bea7b063","abstract_canon_sha256":"3b18c32d70b28e2438be57bdbe89a2f37e5415d44571dbd40c50ee8e661fd018"},"schema_version":"1.0"},"canonical_sha256":"f6e71274c0db5f0c7b9ca4479f36044a14bed9f44f1f03f7b12146aa8ac58549","source":{"kind":"arxiv","id":"1908.03604","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03604","created_at":"2026-07-04T23:52:42Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03604v1","created_at":"2026-07-04T23:52:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03604","created_at":"2026-07-04T23:52:42Z"},{"alias_kind":"pith_short_12","alias_value":"63TRE5GA3NPQ","created_at":"2026-07-04T23:52:42Z"},{"alias_kind":"pith_short_16","alias_value":"63TRE5GA3NPQY644","created_at":"2026-07-04T23:52:42Z"},{"alias_kind":"pith_short_8","alias_value":"63TRE5GA","created_at":"2026-07-04T23:52:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:63TRE5GA3NPQY644URDZ6NQEJI","target":"record","payload":{"canonical_record":{"source":{"id":"1908.03604","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-09T19:25:23Z","cross_cats_sorted":[],"title_canon_sha256":"200d3699518696becb79894cab6934fea00486ffae81d58d0b751d30bea7b063","abstract_canon_sha256":"3b18c32d70b28e2438be57bdbe89a2f37e5415d44571dbd40c50ee8e661fd018"},"schema_version":"1.0"},"canonical_sha256":"f6e71274c0db5f0c7b9ca4479f36044a14bed9f44f1f03f7b12146aa8ac58549","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:52:42.692874Z","signature_b64":"6E6ALXSgTrJYtvt91NjK0Es2zFZjlJeyoApwflfJgR4CqTUc4QX1hzEvDS5rVMv8A++2Wx4NC8XvgXwMrmdvCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6e71274c0db5f0c7b9ca4479f36044a14bed9f44f1f03f7b12146aa8ac58549","last_reissued_at":"2026-07-04T23:52:42.692325Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:52:42.692325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.03604","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":"2026-07-04T23:52:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S/FyQGxyhhCT336PgBGqeOHx6Hcq/fP7pgyfQ6cAOboRicJ3jIXJcMenITVtZ8bVkArscyFklfWaTcL+RC/oBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T12:12:56.878122Z"},"content_sha256":"c63bc215895ea93cf990031c645563fbf924d38b96758f9d9160852cdc696b34","schema_version":"1.0","event_id":"sha256:c63bc215895ea93cf990031c645563fbf924d38b96758f9d9160852cdc696b34"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:63TRE5GA3NPQY644URDZ6NQEJI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional operators via analytic interpolation of integer powers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Evan Camrud","submitted_at":"2019-08-09T19:25:23Z","abstract_excerpt":"Although the study of functional calculus has already established necessary and sufficient conditions for operators to be fractionalized, this paper aims to use our well-conceived notion of integer powers of operators to construct non-integer powers of operators. In doing so, we not only provide a more intuitive understanding of fractional theories, but also provide a framework for producing new fractional theories. Such interpolations allow one to approximate fractional powers by finite sums of integer powers of operators, and thus may find much use in numerical analysis of fractional PDEs an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03604","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/1908.03604/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":"2026-07-04T23:52:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2DgsDTVI8UPJ/VHmFSWU9JXQrmmrFOV2p+ILIC4UsIYAmdZnTcKYAO0ftQ3rn0X2p2CSdDPu/XO7dbxOBR+1DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T12:12:56.878636Z"},"content_sha256":"cb02233d3512d48856cc5f8cde7ec441e818c847196304333040d6858a2fa50c","schema_version":"1.0","event_id":"sha256:cb02233d3512d48856cc5f8cde7ec441e818c847196304333040d6858a2fa50c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/63TRE5GA3NPQY644URDZ6NQEJI/bundle.json","state_url":"https://pith.science/pith/63TRE5GA3NPQY644URDZ6NQEJI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/63TRE5GA3NPQY644URDZ6NQEJI/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":"2026-08-16T12:12:56Z","links":{"resolver":"https://pith.science/pith/63TRE5GA3NPQY644URDZ6NQEJI","bundle":"https://pith.science/pith/63TRE5GA3NPQY644URDZ6NQEJI/bundle.json","state":"https://pith.science/pith/63TRE5GA3NPQY644URDZ6NQEJI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/63TRE5GA3NPQY644URDZ6NQEJI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:63TRE5GA3NPQY644URDZ6NQEJI","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":"3b18c32d70b28e2438be57bdbe89a2f37e5415d44571dbd40c50ee8e661fd018","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-09T19:25:23Z","title_canon_sha256":"200d3699518696becb79894cab6934fea00486ffae81d58d0b751d30bea7b063"},"schema_version":"1.0","source":{"id":"1908.03604","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03604","created_at":"2026-07-04T23:52:42Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03604v1","created_at":"2026-07-04T23:52:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03604","created_at":"2026-07-04T23:52:42Z"},{"alias_kind":"pith_short_12","alias_value":"63TRE5GA3NPQ","created_at":"2026-07-04T23:52:42Z"},{"alias_kind":"pith_short_16","alias_value":"63TRE5GA3NPQY644","created_at":"2026-07-04T23:52:42Z"},{"alias_kind":"pith_short_8","alias_value":"63TRE5GA","created_at":"2026-07-04T23:52:42Z"}],"graph_snapshots":[{"event_id":"sha256:cb02233d3512d48856cc5f8cde7ec441e818c847196304333040d6858a2fa50c","target":"graph","created_at":"2026-07-04T23:52:42Z","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/1908.03604/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Although the study of functional calculus has already established necessary and sufficient conditions for operators to be fractionalized, this paper aims to use our well-conceived notion of integer powers of operators to construct non-integer powers of operators. In doing so, we not only provide a more intuitive understanding of fractional theories, but also provide a framework for producing new fractional theories. Such interpolations allow one to approximate fractional powers by finite sums of integer powers of operators, and thus may find much use in numerical analysis of fractional PDEs an","authors_text":"Evan Camrud","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-09T19:25:23Z","title":"Fractional operators via analytic interpolation of integer powers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03604","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:c63bc215895ea93cf990031c645563fbf924d38b96758f9d9160852cdc696b34","target":"record","created_at":"2026-07-04T23:52:42Z","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":"3b18c32d70b28e2438be57bdbe89a2f37e5415d44571dbd40c50ee8e661fd018","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-09T19:25:23Z","title_canon_sha256":"200d3699518696becb79894cab6934fea00486ffae81d58d0b751d30bea7b063"},"schema_version":"1.0","source":{"id":"1908.03604","kind":"arxiv","version":1}},"canonical_sha256":"f6e71274c0db5f0c7b9ca4479f36044a14bed9f44f1f03f7b12146aa8ac58549","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6e71274c0db5f0c7b9ca4479f36044a14bed9f44f1f03f7b12146aa8ac58549","first_computed_at":"2026-07-04T23:52:42.692325Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:52:42.692325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6E6ALXSgTrJYtvt91NjK0Es2zFZjlJeyoApwflfJgR4CqTUc4QX1hzEvDS5rVMv8A++2Wx4NC8XvgXwMrmdvCA==","signature_status":"signed_v1","signed_at":"2026-07-04T23:52:42.692874Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.03604","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c63bc215895ea93cf990031c645563fbf924d38b96758f9d9160852cdc696b34","sha256:cb02233d3512d48856cc5f8cde7ec441e818c847196304333040d6858a2fa50c"],"state_sha256":"b5882827ffa91f64c5f389f3e322d325a7419fee0e1926f367a1936d2230894f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tWpCfao7kh7F+CkpWAQ3dIaDRwLn6cNXOuX4oE7mXnCBYQDZtLss1X6KcmR5jkwRQO1icQog4alX1sux2x2wCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T12:12:56.883871Z","bundle_sha256":"ac729ca37aa6c254dd93224d442f58e01876a76576d6d21162633f6f7b6036d6"}}