{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4YSUMLIGUXUFICONTEUQG6QDGD","short_pith_number":"pith:4YSUMLIG","canonical_record":{"source":{"id":"1612.07395","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-22T00:12:44Z","cross_cats_sorted":["gr-qc","math.MP"],"title_canon_sha256":"de1e52bfed8c1650625c533d9b14207047743c2cfb927be668e1dbeade3966c0","abstract_canon_sha256":"9b4f832b0a787b322d08e8b0a299e95bb60c2d843506ce38aef9b57e2a37791c"},"schema_version":"1.0"},"canonical_sha256":"e625462d06a5e85409cd9929037a0330d1e9b8cf11ae4ed74f9b67d4493a8338","source":{"kind":"arxiv","id":"1612.07395","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07395","created_at":"2026-05-18T00:46:48Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07395v1","created_at":"2026-05-18T00:46:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07395","created_at":"2026-05-18T00:46:48Z"},{"alias_kind":"pith_short_12","alias_value":"4YSUMLIGUXUF","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4YSUMLIGUXUFICON","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4YSUMLIG","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4YSUMLIGUXUFICONTEUQG6QDGD","target":"record","payload":{"canonical_record":{"source":{"id":"1612.07395","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-22T00:12:44Z","cross_cats_sorted":["gr-qc","math.MP"],"title_canon_sha256":"de1e52bfed8c1650625c533d9b14207047743c2cfb927be668e1dbeade3966c0","abstract_canon_sha256":"9b4f832b0a787b322d08e8b0a299e95bb60c2d843506ce38aef9b57e2a37791c"},"schema_version":"1.0"},"canonical_sha256":"e625462d06a5e85409cd9929037a0330d1e9b8cf11ae4ed74f9b67d4493a8338","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:48.635050Z","signature_b64":"VAQI+7b9GDwjuS6JUwEF86f2QV/LeM/qv/JycMHNm3jdpJ4ppQ8M0/jJdXm9X02FzYD3J+LHczEM5WlfVKJGAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e625462d06a5e85409cd9929037a0330d1e9b8cf11ae4ed74f9b67d4493a8338","last_reissued_at":"2026-05-18T00:46:48.634413Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:48.634413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.07395","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":"2026-05-18T00:46:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"43GaGV0nqEToW8a4FGijXsJ+46szGiH2QCWwQdcSrXNZKSpqcn51/KSP4tTSFJHjLElCw8b5VZ386OTpFR7/CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:37:58.135392Z"},"content_sha256":"891cc5c5a8c5de90fa81cbf53f4a41fcc494a4a6776bc4f2f46f88cb6a0c1887","schema_version":"1.0","event_id":"sha256:891cc5c5a8c5de90fa81cbf53f4a41fcc494a4a6776bc4f2f46f88cb6a0c1887"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4YSUMLIGUXUFICONTEUQG6QDGD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Jacobi-Maupertius metric and Kepler equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math.MP"],"primary_cat":"math-ph","authors_text":"G.W. Gibbons, Partha Guha, Sumanto Chanda","submitted_at":"2016-12-22T00:12:44Z","abstract_excerpt":"This article studies the application of the Jacobi-Eisenhart lift, Jacobi metric and Maupertius transformation to the Kepler system. We start by reviewing fundamentals and the Jacobi metric. Then we study various ways to apply the lift to Kepler related systems: first as conformal description and Bohlin transformation of Hooke's oscillator, second in contact geometry, third in Houri's transformation (Houri, Liouville integrability of Hamiltonian systems and spacetime symmetry, http://www.geocities.jp/football\\_physicien/publication.html), coupled with Milnor's construction (Milnor, The America"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07395","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":"2026-05-18T00:46:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8naa1WJFk4pHCyb3jaVIs7KXjp3VFOt5RFwvinhJYAuIFKa09g/FjSCJN69uSm4F+Q/cE5qq72aLv46jv90XDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:37:58.136136Z"},"content_sha256":"5116dbe24466621352ed532628e7ad331e02dac1b4850817b1d246183c486775","schema_version":"1.0","event_id":"sha256:5116dbe24466621352ed532628e7ad331e02dac1b4850817b1d246183c486775"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4YSUMLIGUXUFICONTEUQG6QDGD/bundle.json","state_url":"https://pith.science/pith/4YSUMLIGUXUFICONTEUQG6QDGD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4YSUMLIGUXUFICONTEUQG6QDGD/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":"2026-05-30T23:37:58Z","links":{"resolver":"https://pith.science/pith/4YSUMLIGUXUFICONTEUQG6QDGD","bundle":"https://pith.science/pith/4YSUMLIGUXUFICONTEUQG6QDGD/bundle.json","state":"https://pith.science/pith/4YSUMLIGUXUFICONTEUQG6QDGD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4YSUMLIGUXUFICONTEUQG6QDGD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4YSUMLIGUXUFICONTEUQG6QDGD","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":"9b4f832b0a787b322d08e8b0a299e95bb60c2d843506ce38aef9b57e2a37791c","cross_cats_sorted":["gr-qc","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-22T00:12:44Z","title_canon_sha256":"de1e52bfed8c1650625c533d9b14207047743c2cfb927be668e1dbeade3966c0"},"schema_version":"1.0","source":{"id":"1612.07395","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07395","created_at":"2026-05-18T00:46:48Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07395v1","created_at":"2026-05-18T00:46:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07395","created_at":"2026-05-18T00:46:48Z"},{"alias_kind":"pith_short_12","alias_value":"4YSUMLIGUXUF","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4YSUMLIGUXUFICON","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4YSUMLIG","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:5116dbe24466621352ed532628e7ad331e02dac1b4850817b1d246183c486775","target":"graph","created_at":"2026-05-18T00:46:48Z","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":"This article studies the application of the Jacobi-Eisenhart lift, Jacobi metric and Maupertius transformation to the Kepler system. We start by reviewing fundamentals and the Jacobi metric. Then we study various ways to apply the lift to Kepler related systems: first as conformal description and Bohlin transformation of Hooke's oscillator, second in contact geometry, third in Houri's transformation (Houri, Liouville integrability of Hamiltonian systems and spacetime symmetry, http://www.geocities.jp/football\\_physicien/publication.html), coupled with Milnor's construction (Milnor, The America","authors_text":"G.W. Gibbons, Partha Guha, Sumanto Chanda","cross_cats":["gr-qc","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-22T00:12:44Z","title":"Jacobi-Maupertius metric and Kepler equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07395","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":"sha256:891cc5c5a8c5de90fa81cbf53f4a41fcc494a4a6776bc4f2f46f88cb6a0c1887","target":"record","created_at":"2026-05-18T00:46:48Z","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":"9b4f832b0a787b322d08e8b0a299e95bb60c2d843506ce38aef9b57e2a37791c","cross_cats_sorted":["gr-qc","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-22T00:12:44Z","title_canon_sha256":"de1e52bfed8c1650625c533d9b14207047743c2cfb927be668e1dbeade3966c0"},"schema_version":"1.0","source":{"id":"1612.07395","kind":"arxiv","version":1}},"canonical_sha256":"e625462d06a5e85409cd9929037a0330d1e9b8cf11ae4ed74f9b67d4493a8338","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e625462d06a5e85409cd9929037a0330d1e9b8cf11ae4ed74f9b67d4493a8338","first_computed_at":"2026-05-18T00:46:48.634413Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:48.634413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VAQI+7b9GDwjuS6JUwEF86f2QV/LeM/qv/JycMHNm3jdpJ4ppQ8M0/jJdXm9X02FzYD3J+LHczEM5WlfVKJGAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:48.635050Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.07395","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:891cc5c5a8c5de90fa81cbf53f4a41fcc494a4a6776bc4f2f46f88cb6a0c1887","sha256:5116dbe24466621352ed532628e7ad331e02dac1b4850817b1d246183c486775"],"state_sha256":"59994e340186763b6122d14ca6e7306f15f7a08db16f93241e4354926fff8cc6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F0sE+BIurhOLy9jVly8LQMvEWJmFEDwGo3cr9874u/TGUGnHefQYFR/t3pgy2ZHCTQ25IcAN+miD/r6cL0MaDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:37:58.139491Z","bundle_sha256":"f5a6f711c37e33f0f2d4f5d74c5d03ba1fc7c320df613a9ead82a78c39deee61"}}