{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:5NYMZM3EI45TMB6Y4DSEDXIVKW","short_pith_number":"pith:5NYMZM3E","canonical_record":{"source":{"id":"1801.05105","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-01-16T03:14:59Z","cross_cats_sorted":[],"title_canon_sha256":"cb11a00afeea996861fc1b0c55c613e624b96f20bd42596219660b4336e278ec","abstract_canon_sha256":"842a662adcc748324084213c57db08e84bf8e51ffbd2f0fa757041206ab41f3c"},"schema_version":"1.0"},"canonical_sha256":"eb70ccb364473b3607d8e0e441dd15558955bc23bb44738127b17d95ff3b9c0e","source":{"kind":"arxiv","id":"1801.05105","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.05105","created_at":"2026-05-17T23:45:58Z"},{"alias_kind":"arxiv_version","alias_value":"1801.05105v2","created_at":"2026-05-17T23:45:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.05105","created_at":"2026-05-17T23:45:58Z"},{"alias_kind":"pith_short_12","alias_value":"5NYMZM3EI45T","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5NYMZM3EI45TMB6Y","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5NYMZM3E","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:5NYMZM3EI45TMB6Y4DSEDXIVKW","target":"record","payload":{"canonical_record":{"source":{"id":"1801.05105","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-01-16T03:14:59Z","cross_cats_sorted":[],"title_canon_sha256":"cb11a00afeea996861fc1b0c55c613e624b96f20bd42596219660b4336e278ec","abstract_canon_sha256":"842a662adcc748324084213c57db08e84bf8e51ffbd2f0fa757041206ab41f3c"},"schema_version":"1.0"},"canonical_sha256":"eb70ccb364473b3607d8e0e441dd15558955bc23bb44738127b17d95ff3b9c0e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:58.184876Z","signature_b64":"2ClC/E3H2nQCbGbUkZt8/rlHH6wM4jyHO/TxGcm6GVAG/q9XLHcbUX1Hp9jlvIrlIUN2LaLkOAaEYPzonTGVAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb70ccb364473b3607d8e0e441dd15558955bc23bb44738127b17d95ff3b9c0e","last_reissued_at":"2026-05-17T23:45:58.184444Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:58.184444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.05105","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":"2026-05-17T23:45:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IAAaKj1zz7O6JeAZcK23Q3XsLBqvnBLP37U3/kgP4S2fqMM4ODrxAXEj6eA2wcgVnUtoqrvNA908wRFnszDHBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T05:46:29.376236Z"},"content_sha256":"a7b423e176289a74f082e139ad1f72905467ae1f5b5e0bfa7bf7b237ad66d10b","schema_version":"1.0","event_id":"sha256:a7b423e176289a74f082e139ad1f72905467ae1f5b5e0bfa7bf7b237ad66d10b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:5NYMZM3EI45TMB6Y4DSEDXIVKW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Second Order Spiral Splines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Lyle Noakes","submitted_at":"2018-01-16T03:14:59Z","abstract_excerpt":"Second order spiral splines are $C^2$ unit-speed planar curves that can be used to interpolate a list $Y$ of $n+1$ points in $\\R ^2$ at times specified in some list $T$, where $n\\geq 2$. Asymptotic methods are used to develop a fast algorithm, based on a pair of tridiagonal linear systems and standard software. The algorithm constructs a second order spiral spline interpolant for data that is convex and sufficiently finely sampled."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05105","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":"2026-05-17T23:45:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"REsQLpdPB7Ev78eApXtU+QVKYguQG9s7hQs5xmRY39varPqanBlwc/Mt4qILhJYNGSLBzYU2GyGGop1abYXsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T05:46:29.376640Z"},"content_sha256":"f27071579e5b5aaafec321dfebf75d103864b9cde468aa74b7f75f6cb1a8fa66","schema_version":"1.0","event_id":"sha256:f27071579e5b5aaafec321dfebf75d103864b9cde468aa74b7f75f6cb1a8fa66"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5NYMZM3EI45TMB6Y4DSEDXIVKW/bundle.json","state_url":"https://pith.science/pith/5NYMZM3EI45TMB6Y4DSEDXIVKW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5NYMZM3EI45TMB6Y4DSEDXIVKW/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":"2026-06-30T05:46:29Z","links":{"resolver":"https://pith.science/pith/5NYMZM3EI45TMB6Y4DSEDXIVKW","bundle":"https://pith.science/pith/5NYMZM3EI45TMB6Y4DSEDXIVKW/bundle.json","state":"https://pith.science/pith/5NYMZM3EI45TMB6Y4DSEDXIVKW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5NYMZM3EI45TMB6Y4DSEDXIVKW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5NYMZM3EI45TMB6Y4DSEDXIVKW","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":"842a662adcc748324084213c57db08e84bf8e51ffbd2f0fa757041206ab41f3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-01-16T03:14:59Z","title_canon_sha256":"cb11a00afeea996861fc1b0c55c613e624b96f20bd42596219660b4336e278ec"},"schema_version":"1.0","source":{"id":"1801.05105","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.05105","created_at":"2026-05-17T23:45:58Z"},{"alias_kind":"arxiv_version","alias_value":"1801.05105v2","created_at":"2026-05-17T23:45:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.05105","created_at":"2026-05-17T23:45:58Z"},{"alias_kind":"pith_short_12","alias_value":"5NYMZM3EI45T","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5NYMZM3EI45TMB6Y","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5NYMZM3E","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:f27071579e5b5aaafec321dfebf75d103864b9cde468aa74b7f75f6cb1a8fa66","target":"graph","created_at":"2026-05-17T23:45:58Z","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":"Second order spiral splines are $C^2$ unit-speed planar curves that can be used to interpolate a list $Y$ of $n+1$ points in $\\R ^2$ at times specified in some list $T$, where $n\\geq 2$. Asymptotic methods are used to develop a fast algorithm, based on a pair of tridiagonal linear systems and standard software. The algorithm constructs a second order spiral spline interpolant for data that is convex and sufficiently finely sampled.","authors_text":"Lyle Noakes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-01-16T03:14:59Z","title":"Second Order Spiral Splines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05105","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:a7b423e176289a74f082e139ad1f72905467ae1f5b5e0bfa7bf7b237ad66d10b","target":"record","created_at":"2026-05-17T23:45:58Z","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":"842a662adcc748324084213c57db08e84bf8e51ffbd2f0fa757041206ab41f3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-01-16T03:14:59Z","title_canon_sha256":"cb11a00afeea996861fc1b0c55c613e624b96f20bd42596219660b4336e278ec"},"schema_version":"1.0","source":{"id":"1801.05105","kind":"arxiv","version":2}},"canonical_sha256":"eb70ccb364473b3607d8e0e441dd15558955bc23bb44738127b17d95ff3b9c0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb70ccb364473b3607d8e0e441dd15558955bc23bb44738127b17d95ff3b9c0e","first_computed_at":"2026-05-17T23:45:58.184444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:58.184444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2ClC/E3H2nQCbGbUkZt8/rlHH6wM4jyHO/TxGcm6GVAG/q9XLHcbUX1Hp9jlvIrlIUN2LaLkOAaEYPzonTGVAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:58.184876Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.05105","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7b423e176289a74f082e139ad1f72905467ae1f5b5e0bfa7bf7b237ad66d10b","sha256:f27071579e5b5aaafec321dfebf75d103864b9cde468aa74b7f75f6cb1a8fa66"],"state_sha256":"4286aff3fe2ec4b731b6a0158492bf4a65ba5e873267d148637880b70ad79101"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FBtZ9jOqNUzfqDexXvQriTaXS5mdz8W9WOBoxia3+qsXOPpY8s2M0vRfZhq/vSt49YoX6N6MVAh9WkMA0+y3CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T05:46:29.378862Z","bundle_sha256":"227d5fb58b6a7daf35145a4320cae8d242288607aaf2700e2c3b9ba95be27847"}}