{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CWDTRLDPVL3TL5G3YORZOGWBKP","short_pith_number":"pith:CWDTRLDP","canonical_record":{"source":{"id":"1608.00616","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2016-07-29T11:26:38Z","cross_cats_sorted":[],"title_canon_sha256":"2e058231f209e8f3ba9cd96f0fee05bd7005a17bf3f89ac143224ae2e5d079c7","abstract_canon_sha256":"1659b4605fb773304496d3fbe6bfa1375b2459fea317ffcad328703e28d0ad45"},"schema_version":"1.0"},"canonical_sha256":"158738ac6faaf735f4dbc3a3971ac153f3356baca6c732bca6956edb299c1ad6","source":{"kind":"arxiv","id":"1608.00616","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00616","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00616v1","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00616","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"pith_short_12","alias_value":"CWDTRLDPVL3T","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CWDTRLDPVL3TL5G3","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CWDTRLDP","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CWDTRLDPVL3TL5G3YORZOGWBKP","target":"record","payload":{"canonical_record":{"source":{"id":"1608.00616","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2016-07-29T11:26:38Z","cross_cats_sorted":[],"title_canon_sha256":"2e058231f209e8f3ba9cd96f0fee05bd7005a17bf3f89ac143224ae2e5d079c7","abstract_canon_sha256":"1659b4605fb773304496d3fbe6bfa1375b2459fea317ffcad328703e28d0ad45"},"schema_version":"1.0"},"canonical_sha256":"158738ac6faaf735f4dbc3a3971ac153f3356baca6c732bca6956edb299c1ad6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:11.378364Z","signature_b64":"wEMpU1P08FmCZuDc5v9aOZwfv3jsC4FRACye9kwVgqbkaADBnhLMSa/tHt9C0u8jgfmOdzKcZXPz34h6sutJBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"158738ac6faaf735f4dbc3a3971ac153f3356baca6c732bca6956edb299c1ad6","last_reissued_at":"2026-05-18T01:10:11.377939Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:11.377939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.00616","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":"2026-05-18T01:10:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hlc4/yTAhNQxLUK1yYx+4dNIrFLXdIz1TSP/FriXeLKM352rpXMiPnjHOQzdsQZxzXeNoVRyyseuHbGRZa7uCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:49:43.297308Z"},"content_sha256":"a5e5e8372e28c119aeb7deb70bb1eb59e4c4f7993faa248789571717406a0d1c","schema_version":"1.0","event_id":"sha256:a5e5e8372e28c119aeb7deb70bb1eb59e4c4f7993faa248789571717406a0d1c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CWDTRLDPVL3TL5G3YORZOGWBKP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The classical harmonic chain: solution via Laplace transforms and continued fractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.class-ph","authors_text":"Nick Kwidzinski, Ralf Bulla","submitted_at":"2016-07-29T11:26:38Z","abstract_excerpt":"The harmonic chain is a classical many-particle system which can be solved exactly for arbitrary number of particles (at least in simple cases, such as equal masses and spring constants). A nice feature of the harmonic chain is that the final result for the displacements of the individual particles can be easily understood -- therefore, this example fits well into a course of classical mechanics for undergraduates. Here we show how to calculate the displacements by solving equations of motion for the Laplace transforms $\\mathcal{L}\\left\\{q_n\\right\\}(s)$ of the displacements $q_n(t)$. This lead"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00616","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":"2026-05-18T01:10:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/srhvaE+CdXDmMb7F9m+0ISxV29ZnWsPFNNvEbvPHzwFk0cdafEyF4B11jMY92fdwHEw5lHbma7M+piSmwHGBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:49:43.297975Z"},"content_sha256":"e69ea2d1bc472a6951bc6fcfc3ab7f81c0b203615c35fde81f87dc3aef61721a","schema_version":"1.0","event_id":"sha256:e69ea2d1bc472a6951bc6fcfc3ab7f81c0b203615c35fde81f87dc3aef61721a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CWDTRLDPVL3TL5G3YORZOGWBKP/bundle.json","state_url":"https://pith.science/pith/CWDTRLDPVL3TL5G3YORZOGWBKP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CWDTRLDPVL3TL5G3YORZOGWBKP/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":"2026-05-28T20:49:43Z","links":{"resolver":"https://pith.science/pith/CWDTRLDPVL3TL5G3YORZOGWBKP","bundle":"https://pith.science/pith/CWDTRLDPVL3TL5G3YORZOGWBKP/bundle.json","state":"https://pith.science/pith/CWDTRLDPVL3TL5G3YORZOGWBKP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CWDTRLDPVL3TL5G3YORZOGWBKP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CWDTRLDPVL3TL5G3YORZOGWBKP","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":"1659b4605fb773304496d3fbe6bfa1375b2459fea317ffcad328703e28d0ad45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2016-07-29T11:26:38Z","title_canon_sha256":"2e058231f209e8f3ba9cd96f0fee05bd7005a17bf3f89ac143224ae2e5d079c7"},"schema_version":"1.0","source":{"id":"1608.00616","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00616","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00616v1","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00616","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"pith_short_12","alias_value":"CWDTRLDPVL3T","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CWDTRLDPVL3TL5G3","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CWDTRLDP","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:e69ea2d1bc472a6951bc6fcfc3ab7f81c0b203615c35fde81f87dc3aef61721a","target":"graph","created_at":"2026-05-18T01:10:11Z","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":"The harmonic chain is a classical many-particle system which can be solved exactly for arbitrary number of particles (at least in simple cases, such as equal masses and spring constants). A nice feature of the harmonic chain is that the final result for the displacements of the individual particles can be easily understood -- therefore, this example fits well into a course of classical mechanics for undergraduates. Here we show how to calculate the displacements by solving equations of motion for the Laplace transforms $\\mathcal{L}\\left\\{q_n\\right\\}(s)$ of the displacements $q_n(t)$. This lead","authors_text":"Nick Kwidzinski, Ralf Bulla","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2016-07-29T11:26:38Z","title":"The classical harmonic chain: solution via Laplace transforms and continued fractions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00616","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:a5e5e8372e28c119aeb7deb70bb1eb59e4c4f7993faa248789571717406a0d1c","target":"record","created_at":"2026-05-18T01:10:11Z","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":"1659b4605fb773304496d3fbe6bfa1375b2459fea317ffcad328703e28d0ad45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2016-07-29T11:26:38Z","title_canon_sha256":"2e058231f209e8f3ba9cd96f0fee05bd7005a17bf3f89ac143224ae2e5d079c7"},"schema_version":"1.0","source":{"id":"1608.00616","kind":"arxiv","version":1}},"canonical_sha256":"158738ac6faaf735f4dbc3a3971ac153f3356baca6c732bca6956edb299c1ad6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"158738ac6faaf735f4dbc3a3971ac153f3356baca6c732bca6956edb299c1ad6","first_computed_at":"2026-05-18T01:10:11.377939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:11.377939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wEMpU1P08FmCZuDc5v9aOZwfv3jsC4FRACye9kwVgqbkaADBnhLMSa/tHt9C0u8jgfmOdzKcZXPz34h6sutJBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:11.378364Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.00616","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5e5e8372e28c119aeb7deb70bb1eb59e4c4f7993faa248789571717406a0d1c","sha256:e69ea2d1bc472a6951bc6fcfc3ab7f81c0b203615c35fde81f87dc3aef61721a"],"state_sha256":"c1397791ae5918c2079a0d2ba9d663688e18a62f5daf9fa9b8a0d865896f73c7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j8BWj9161MQJf838gi0p92ow+yNRaxYQ6uIzS4y9VwFvJsxGEk1GVlloPVTjubPkWrae0UnMTSLjwvtJVMjtAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:49:43.301509Z","bundle_sha256":"e8d0e69641fca6175219c62d9f01fc35805ff7be335e10499d210d2b4e64a49e"}}