{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NFCQ4XC65YEZKTOJTIAHHWWKBO","short_pith_number":"pith:NFCQ4XC6","canonical_record":{"source":{"id":"1609.08006","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-09-23T11:58:49Z","cross_cats_sorted":[],"title_canon_sha256":"7f629933ae28f955d764291bfc1dec0b7880c6bcc147e87807a875cf69e7676c","abstract_canon_sha256":"8fd67289a3503a2a985ce8fcb214e86fbffa14a84cd4f9d04d9ed3f6a63c1708"},"schema_version":"1.0"},"canonical_sha256":"69450e5c5eee09954dc99a0073daca0bbd60cd19bc80dee39e2a18996bee9bce","source":{"kind":"arxiv","id":"1609.08006","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.08006","created_at":"2026-05-18T01:03:54Z"},{"alias_kind":"arxiv_version","alias_value":"1609.08006v1","created_at":"2026-05-18T01:03:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08006","created_at":"2026-05-18T01:03:54Z"},{"alias_kind":"pith_short_12","alias_value":"NFCQ4XC65YEZ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NFCQ4XC65YEZKTOJ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NFCQ4XC6","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NFCQ4XC65YEZKTOJTIAHHWWKBO","target":"record","payload":{"canonical_record":{"source":{"id":"1609.08006","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-09-23T11:58:49Z","cross_cats_sorted":[],"title_canon_sha256":"7f629933ae28f955d764291bfc1dec0b7880c6bcc147e87807a875cf69e7676c","abstract_canon_sha256":"8fd67289a3503a2a985ce8fcb214e86fbffa14a84cd4f9d04d9ed3f6a63c1708"},"schema_version":"1.0"},"canonical_sha256":"69450e5c5eee09954dc99a0073daca0bbd60cd19bc80dee39e2a18996bee9bce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:54.678420Z","signature_b64":"iVkoHdc53MNcYK8uOlj7Kul8wqqcEbb5sslx7lVPwtl4v1kzmEiArQYVxjYfDX0YBtjmPaifF7MWfsDaJdM8Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69450e5c5eee09954dc99a0073daca0bbd60cd19bc80dee39e2a18996bee9bce","last_reissued_at":"2026-05-18T01:03:54.677721Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:54.677721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.08006","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":"2026-05-18T01:03:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W71rmJRbjN05Se9Kx5qAuPG1ljU0D0sCuVt5djYk6Tw8ZDzGiYabp0bBz16/MmE1SX5aSJ0Vl9SKBTBadaLuCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:53:28.019420Z"},"content_sha256":"bd4b77dee28408090552c72a6207f26436bb8397e61c9970bd1b51b5c56b71b8","schema_version":"1.0","event_id":"sha256:bd4b77dee28408090552c72a6207f26436bb8397e61c9970bd1b51b5c56b71b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NFCQ4XC65YEZKTOJTIAHHWWKBO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hermite Calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"B. Germano, G. Dattoli, M. R. Martinelli, S. Licciardi","submitted_at":"2016-09-23T11:58:49Z","abstract_excerpt":"We develop a new method of umbral nature to treat blocks of Hermite and of Hermite like polynomials as independent algebraic quantities. The Calculus we propose allows the formulation of a number of practical rules allowing significant simplifications in computational problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08006","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":"2026-05-18T01:03:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yrLuItKPN/Rvyzzb6LWZe59Ebazr4EbWKEtmXcBYdCEeIFKQKxXI+5V7xeJjI0RwyqX3qa/8UDDfclPJqL1nCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:53:28.019764Z"},"content_sha256":"95aa8c07d0dfde9cd529cc8cbf966b31108b4f22d250c3a4b80755fdaec41375","schema_version":"1.0","event_id":"sha256:95aa8c07d0dfde9cd529cc8cbf966b31108b4f22d250c3a4b80755fdaec41375"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NFCQ4XC65YEZKTOJTIAHHWWKBO/bundle.json","state_url":"https://pith.science/pith/NFCQ4XC65YEZKTOJTIAHHWWKBO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NFCQ4XC65YEZKTOJTIAHHWWKBO/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":"2026-06-01T13:53:28Z","links":{"resolver":"https://pith.science/pith/NFCQ4XC65YEZKTOJTIAHHWWKBO","bundle":"https://pith.science/pith/NFCQ4XC65YEZKTOJTIAHHWWKBO/bundle.json","state":"https://pith.science/pith/NFCQ4XC65YEZKTOJTIAHHWWKBO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NFCQ4XC65YEZKTOJTIAHHWWKBO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NFCQ4XC65YEZKTOJTIAHHWWKBO","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":"8fd67289a3503a2a985ce8fcb214e86fbffa14a84cd4f9d04d9ed3f6a63c1708","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-09-23T11:58:49Z","title_canon_sha256":"7f629933ae28f955d764291bfc1dec0b7880c6bcc147e87807a875cf69e7676c"},"schema_version":"1.0","source":{"id":"1609.08006","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.08006","created_at":"2026-05-18T01:03:54Z"},{"alias_kind":"arxiv_version","alias_value":"1609.08006v1","created_at":"2026-05-18T01:03:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08006","created_at":"2026-05-18T01:03:54Z"},{"alias_kind":"pith_short_12","alias_value":"NFCQ4XC65YEZ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NFCQ4XC65YEZKTOJ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NFCQ4XC6","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:95aa8c07d0dfde9cd529cc8cbf966b31108b4f22d250c3a4b80755fdaec41375","target":"graph","created_at":"2026-05-18T01:03:54Z","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 develop a new method of umbral nature to treat blocks of Hermite and of Hermite like polynomials as independent algebraic quantities. The Calculus we propose allows the formulation of a number of practical rules allowing significant simplifications in computational problems.","authors_text":"B. Germano, G. Dattoli, M. R. Martinelli, S. Licciardi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-09-23T11:58:49Z","title":"Hermite Calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08006","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:bd4b77dee28408090552c72a6207f26436bb8397e61c9970bd1b51b5c56b71b8","target":"record","created_at":"2026-05-18T01:03:54Z","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":"8fd67289a3503a2a985ce8fcb214e86fbffa14a84cd4f9d04d9ed3f6a63c1708","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-09-23T11:58:49Z","title_canon_sha256":"7f629933ae28f955d764291bfc1dec0b7880c6bcc147e87807a875cf69e7676c"},"schema_version":"1.0","source":{"id":"1609.08006","kind":"arxiv","version":1}},"canonical_sha256":"69450e5c5eee09954dc99a0073daca0bbd60cd19bc80dee39e2a18996bee9bce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69450e5c5eee09954dc99a0073daca0bbd60cd19bc80dee39e2a18996bee9bce","first_computed_at":"2026-05-18T01:03:54.677721Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:54.677721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iVkoHdc53MNcYK8uOlj7Kul8wqqcEbb5sslx7lVPwtl4v1kzmEiArQYVxjYfDX0YBtjmPaifF7MWfsDaJdM8Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:54.678420Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.08006","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd4b77dee28408090552c72a6207f26436bb8397e61c9970bd1b51b5c56b71b8","sha256:95aa8c07d0dfde9cd529cc8cbf966b31108b4f22d250c3a4b80755fdaec41375"],"state_sha256":"43d1fe1065e20ab82b52c04de56a2e53c68f2c27281f21e072a0f7c7b1d73ee4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cq38IwGo4uamPOJ4M0aVJxGTerXjT3JTvjbSmy4RGMzO8KDkwYrOPAKoxqw9a+OCPx/ElDtNoXK6h/TJxY+tDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T13:53:28.021618Z","bundle_sha256":"c52d9cf78beab6df30969e890e9f23f0c66a4c294281207b2ef5415a3ab16960"}}