{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:FMK5VLFDE7M2RBYKL7USFU473V","short_pith_number":"pith:FMK5VLFD","canonical_record":{"source":{"id":"1407.1108","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-07-04T01:35:01Z","cross_cats_sorted":[],"title_canon_sha256":"9d183286b617a44d1f630202b48f5dc11721911d648563c9451e6bb7f2195d54","abstract_canon_sha256":"e90adde3bc7d5b9363babd41aa7e8c75dc44909588fb2d2d7fedbcca711b003b"},"schema_version":"1.0"},"canonical_sha256":"2b15daaca327d9a8870a5fe922d39fdd73fb70a5d5146e375897d30f4570e12b","source":{"kind":"arxiv","id":"1407.1108","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1108","created_at":"2026-05-18T00:53:19Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1108v4","created_at":"2026-05-18T00:53:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1108","created_at":"2026-05-18T00:53:19Z"},{"alias_kind":"pith_short_12","alias_value":"FMK5VLFDE7M2","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FMK5VLFDE7M2RBYK","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FMK5VLFD","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:FMK5VLFDE7M2RBYKL7USFU473V","target":"record","payload":{"canonical_record":{"source":{"id":"1407.1108","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-07-04T01:35:01Z","cross_cats_sorted":[],"title_canon_sha256":"9d183286b617a44d1f630202b48f5dc11721911d648563c9451e6bb7f2195d54","abstract_canon_sha256":"e90adde3bc7d5b9363babd41aa7e8c75dc44909588fb2d2d7fedbcca711b003b"},"schema_version":"1.0"},"canonical_sha256":"2b15daaca327d9a8870a5fe922d39fdd73fb70a5d5146e375897d30f4570e12b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:19.500726Z","signature_b64":"mmTQo7g72hST0oF3Ry6ZQP7HumQRv8aQsv7ZYxFD55hR6Ull8y/lAQpjr7w6MM6Wzn+Yo0MEAjEclrFdlstvDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b15daaca327d9a8870a5fe922d39fdd73fb70a5d5146e375897d30f4570e12b","last_reissued_at":"2026-05-18T00:53:19.500266Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:19.500266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.1108","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"odL5e6arEjQTjM/6C+po5UhY5Pblxd4x0bEGi+mhF6GPHjzWCqRhA0tVKIaoay8qTxG1yrYG8Mh+HTDdlrgqCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T01:20:29.009506Z"},"content_sha256":"3a53e54b0c3a60618b31a28c64f54157da06064631f0bb5d5e7c0b7f4d397490","schema_version":"1.0","event_id":"sha256:3a53e54b0c3a60618b31a28c64f54157da06064631f0bb5d5e7c0b7f4d397490"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:FMK5VLFDE7M2RBYKL7USFU473V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A New Family of Regularized Kernels for the Harmonic Oscillator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Andrew Christlieb, Benjamin Ong, Bryan Quaife","submitted_at":"2014-07-04T01:35:01Z","abstract_excerpt":"In this paper, a new two-parameter family of regularized kernels is introduced, suitable for applying high-order time stepping to N-body systems. These high-order kernels are derived by truncating a Taylor expansion of the non-regularized kernel about $(r^2+\\epsilon^2)$, generating a sequence of increasingly more accurate kernels. This paper proves the validity of this two-parameter family of regularized kernels, constructs error estimates, and illustrates the benefits of using high-order kernels through numerical experiments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1108","kind":"arxiv","version":4},"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":"2026-05-18T00:53:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I/TLJCLADbtAMk6HHAiBCpE9rlxFnE4EmRIM2B9M1T8pbBTFB33BuFaC04kSHNPIESvpxL2DzhKx7/s+fKOPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T01:20:29.009850Z"},"content_sha256":"19d0f0ed0f4494e49196c8ae6a2108e8de947cfab999bf6f9e2d9a7b6a9647b5","schema_version":"1.0","event_id":"sha256:19d0f0ed0f4494e49196c8ae6a2108e8de947cfab999bf6f9e2d9a7b6a9647b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FMK5VLFDE7M2RBYKL7USFU473V/bundle.json","state_url":"https://pith.science/pith/FMK5VLFDE7M2RBYKL7USFU473V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FMK5VLFDE7M2RBYKL7USFU473V/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":"2026-06-22T01:20:29Z","links":{"resolver":"https://pith.science/pith/FMK5VLFDE7M2RBYKL7USFU473V","bundle":"https://pith.science/pith/FMK5VLFDE7M2RBYKL7USFU473V/bundle.json","state":"https://pith.science/pith/FMK5VLFDE7M2RBYKL7USFU473V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FMK5VLFDE7M2RBYKL7USFU473V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FMK5VLFDE7M2RBYKL7USFU473V","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":"e90adde3bc7d5b9363babd41aa7e8c75dc44909588fb2d2d7fedbcca711b003b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-07-04T01:35:01Z","title_canon_sha256":"9d183286b617a44d1f630202b48f5dc11721911d648563c9451e6bb7f2195d54"},"schema_version":"1.0","source":{"id":"1407.1108","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1108","created_at":"2026-05-18T00:53:19Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1108v4","created_at":"2026-05-18T00:53:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1108","created_at":"2026-05-18T00:53:19Z"},{"alias_kind":"pith_short_12","alias_value":"FMK5VLFDE7M2","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FMK5VLFDE7M2RBYK","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FMK5VLFD","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:19d0f0ed0f4494e49196c8ae6a2108e8de947cfab999bf6f9e2d9a7b6a9647b5","target":"graph","created_at":"2026-05-18T00:53:19Z","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":"In this paper, a new two-parameter family of regularized kernels is introduced, suitable for applying high-order time stepping to N-body systems. These high-order kernels are derived by truncating a Taylor expansion of the non-regularized kernel about $(r^2+\\epsilon^2)$, generating a sequence of increasingly more accurate kernels. This paper proves the validity of this two-parameter family of regularized kernels, constructs error estimates, and illustrates the benefits of using high-order kernels through numerical experiments.","authors_text":"Andrew Christlieb, Benjamin Ong, Bryan Quaife","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-07-04T01:35:01Z","title":"A New Family of Regularized Kernels for the Harmonic Oscillator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1108","kind":"arxiv","version":4},"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":"sha256:3a53e54b0c3a60618b31a28c64f54157da06064631f0bb5d5e7c0b7f4d397490","target":"record","created_at":"2026-05-18T00:53:19Z","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":"e90adde3bc7d5b9363babd41aa7e8c75dc44909588fb2d2d7fedbcca711b003b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-07-04T01:35:01Z","title_canon_sha256":"9d183286b617a44d1f630202b48f5dc11721911d648563c9451e6bb7f2195d54"},"schema_version":"1.0","source":{"id":"1407.1108","kind":"arxiv","version":4}},"canonical_sha256":"2b15daaca327d9a8870a5fe922d39fdd73fb70a5d5146e375897d30f4570e12b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b15daaca327d9a8870a5fe922d39fdd73fb70a5d5146e375897d30f4570e12b","first_computed_at":"2026-05-18T00:53:19.500266Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:19.500266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mmTQo7g72hST0oF3Ry6ZQP7HumQRv8aQsv7ZYxFD55hR6Ull8y/lAQpjr7w6MM6Wzn+Yo0MEAjEclrFdlstvDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:19.500726Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.1108","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a53e54b0c3a60618b31a28c64f54157da06064631f0bb5d5e7c0b7f4d397490","sha256:19d0f0ed0f4494e49196c8ae6a2108e8de947cfab999bf6f9e2d9a7b6a9647b5"],"state_sha256":"04553618a215ad4199b7f0aecbf9d14c897f38ac4da5532f4f7ea4cb8b6b611e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CU+3j4WQMcAG6onKijpYvz/DwLTpUGqi4rTYsVkz7+yNjgYkug4Y5JIvHx7Sqh0YD1j6bLVeQRw8ub3oRVVZCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T01:20:29.011662Z","bundle_sha256":"5386b7ec8a42c72f04cd1d1b8ec7431ea1b108a5b7d1ad7b2cb2fa00f7e9f9ec"}}