{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:2D7WVBJHR5WINX7RZH43OTBBMK","short_pith_number":"pith:2D7WVBJH","canonical_record":{"source":{"id":"1205.5299","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2012-05-23T22:03:25Z","cross_cats_sorted":[],"title_canon_sha256":"c8790426dcca11923146bde78633010502dfd4df5239d37e6b8564e6547d7689","abstract_canon_sha256":"e1f16f8ce8d2cc81d42e17c7ff3f77763844893b0840ff213a5899f33b732958"},"schema_version":"1.0"},"canonical_sha256":"d0ff6a85278f6c86dff1c9f9b74c2162bb9ccab55ba7118333f9f166f4cbb4f4","source":{"kind":"arxiv","id":"1205.5299","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5299","created_at":"2026-05-18T01:57:18Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5299v1","created_at":"2026-05-18T01:57:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5299","created_at":"2026-05-18T01:57:18Z"},{"alias_kind":"pith_short_12","alias_value":"2D7WVBJHR5WI","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2D7WVBJHR5WINX7R","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2D7WVBJH","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:2D7WVBJHR5WINX7RZH43OTBBMK","target":"record","payload":{"canonical_record":{"source":{"id":"1205.5299","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2012-05-23T22:03:25Z","cross_cats_sorted":[],"title_canon_sha256":"c8790426dcca11923146bde78633010502dfd4df5239d37e6b8564e6547d7689","abstract_canon_sha256":"e1f16f8ce8d2cc81d42e17c7ff3f77763844893b0840ff213a5899f33b732958"},"schema_version":"1.0"},"canonical_sha256":"d0ff6a85278f6c86dff1c9f9b74c2162bb9ccab55ba7118333f9f166f4cbb4f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:18.172487Z","signature_b64":"tBZsu+bSzjxGeIZQwtFAheGMrEw4Y5ccN69+BonMAxyGGwmVanTaAjj87cTP7+tMjnLPcGQb3NqRKEEhmcKjAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0ff6a85278f6c86dff1c9f9b74c2162bb9ccab55ba7118333f9f166f4cbb4f4","last_reissued_at":"2026-05-18T01:57:18.171849Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:18.171849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.5299","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":"2026-05-18T01:57:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BZV2FnkJzHQWO/DWmvyUoGSYVapTioldIvaQSyGUctbQStqPO/EeJ9JXMH7GTAYLGSu2zCmEoCIY3u2RCSRdDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T08:25:48.115713Z"},"content_sha256":"bcef667f2bfb370315f8b7b844e805958132010a22f51af236fda4af0a9e5c89","schema_version":"1.0","event_id":"sha256:bcef667f2bfb370315f8b7b844e805958132010a22f51af236fda4af0a9e5c89"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:2D7WVBJHR5WINX7RZH43OTBBMK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relativistic Linear Restoring Force","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.class-ph","authors_text":"D. Clark, J. Franklin, N. Mann","submitted_at":"2012-05-23T22:03:25Z","abstract_excerpt":"We consider two different forms for a relativistic version of a linear restoring force. The pair comes from taking Hooke's law to be the force appearing on the right of the relativistic expressions: dp/dt or dp/dtau . Either formulation recovers Hooke's law in the non-relativistic limit. In addition to these two forces, we introduce a form of retardation appropriate for the description of a linear (in displacement) force arising from the interaction of a pair of particles with a relativistic field. The procedure is akin to replacing Coulomb's law in E&M with a retarded form (the first correcti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5299","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":"2026-05-18T01:57:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+lybxt9UVbg8i7tf90/7QlZlox7zBDXuCJftBHA8G8ZbhxnPpF4NbRGkgkEnWLL4NzFPARNHKaRJA15NCa9lDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T08:25:48.116440Z"},"content_sha256":"f934b20bcd19750ff4b9bea121a443adea09fbf58e466a9b23db72843acd24fc","schema_version":"1.0","event_id":"sha256:f934b20bcd19750ff4b9bea121a443adea09fbf58e466a9b23db72843acd24fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2D7WVBJHR5WINX7RZH43OTBBMK/bundle.json","state_url":"https://pith.science/pith/2D7WVBJHR5WINX7RZH43OTBBMK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2D7WVBJHR5WINX7RZH43OTBBMK/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":"2026-05-23T08:25:48Z","links":{"resolver":"https://pith.science/pith/2D7WVBJHR5WINX7RZH43OTBBMK","bundle":"https://pith.science/pith/2D7WVBJHR5WINX7RZH43OTBBMK/bundle.json","state":"https://pith.science/pith/2D7WVBJHR5WINX7RZH43OTBBMK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2D7WVBJHR5WINX7RZH43OTBBMK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2D7WVBJHR5WINX7RZH43OTBBMK","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":"e1f16f8ce8d2cc81d42e17c7ff3f77763844893b0840ff213a5899f33b732958","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2012-05-23T22:03:25Z","title_canon_sha256":"c8790426dcca11923146bde78633010502dfd4df5239d37e6b8564e6547d7689"},"schema_version":"1.0","source":{"id":"1205.5299","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5299","created_at":"2026-05-18T01:57:18Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5299v1","created_at":"2026-05-18T01:57:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5299","created_at":"2026-05-18T01:57:18Z"},{"alias_kind":"pith_short_12","alias_value":"2D7WVBJHR5WI","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2D7WVBJHR5WINX7R","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2D7WVBJH","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:f934b20bcd19750ff4b9bea121a443adea09fbf58e466a9b23db72843acd24fc","target":"graph","created_at":"2026-05-18T01:57:18Z","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 consider two different forms for a relativistic version of a linear restoring force. The pair comes from taking Hooke's law to be the force appearing on the right of the relativistic expressions: dp/dt or dp/dtau . Either formulation recovers Hooke's law in the non-relativistic limit. In addition to these two forces, we introduce a form of retardation appropriate for the description of a linear (in displacement) force arising from the interaction of a pair of particles with a relativistic field. The procedure is akin to replacing Coulomb's law in E&M with a retarded form (the first correcti","authors_text":"D. Clark, J. Franklin, N. Mann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2012-05-23T22:03:25Z","title":"Relativistic Linear Restoring Force"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5299","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:bcef667f2bfb370315f8b7b844e805958132010a22f51af236fda4af0a9e5c89","target":"record","created_at":"2026-05-18T01:57:18Z","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":"e1f16f8ce8d2cc81d42e17c7ff3f77763844893b0840ff213a5899f33b732958","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2012-05-23T22:03:25Z","title_canon_sha256":"c8790426dcca11923146bde78633010502dfd4df5239d37e6b8564e6547d7689"},"schema_version":"1.0","source":{"id":"1205.5299","kind":"arxiv","version":1}},"canonical_sha256":"d0ff6a85278f6c86dff1c9f9b74c2162bb9ccab55ba7118333f9f166f4cbb4f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0ff6a85278f6c86dff1c9f9b74c2162bb9ccab55ba7118333f9f166f4cbb4f4","first_computed_at":"2026-05-18T01:57:18.171849Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:18.171849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tBZsu+bSzjxGeIZQwtFAheGMrEw4Y5ccN69+BonMAxyGGwmVanTaAjj87cTP7+tMjnLPcGQb3NqRKEEhmcKjAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:18.172487Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.5299","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bcef667f2bfb370315f8b7b844e805958132010a22f51af236fda4af0a9e5c89","sha256:f934b20bcd19750ff4b9bea121a443adea09fbf58e466a9b23db72843acd24fc"],"state_sha256":"4332523bc86e9854ac9209ec7fb88f5db19fd1b3ec135847e21ae172a4a2bc18"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cMDEZoeOJey2pchNB0jfkwCYml40YlZ6uZqpDRvoMGSX/GhM+sqDTKl/9zBUEcnKkDFn9lkmhtPxOW9SgrdHAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T08:25:48.120538Z","bundle_sha256":"48797a3313a9bf27a11bb6b821fdeb18d88ff9cbccc2074ca6852e445cffe9b4"}}