{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3VCBIMTXYCQ27EAAGJFF4A5BUV","short_pith_number":"pith:3VCBIMTX","canonical_record":{"source":{"id":"1407.7163","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DS","submitted_at":"2014-07-26T22:44:07Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"16308ee513e22a3ba4cad47e2c5ad20be231f6ae94588fe6659d1bb3f40a5271","abstract_canon_sha256":"b8e8ef1419b773a511679e37b6127f961f7275cbd3d3f9109e2452a792f76eb1"},"schema_version":"1.0"},"canonical_sha256":"dd44143277c0a1af9000324a5e03a1a540c43bb40cf411ace2923a525b0d8950","source":{"kind":"arxiv","id":"1407.7163","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.7163","created_at":"2026-05-18T02:37:51Z"},{"alias_kind":"arxiv_version","alias_value":"1407.7163v2","created_at":"2026-05-18T02:37:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7163","created_at":"2026-05-18T02:37:51Z"},{"alias_kind":"pith_short_12","alias_value":"3VCBIMTXYCQ2","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3VCBIMTXYCQ27EAA","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3VCBIMTX","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3VCBIMTXYCQ27EAAGJFF4A5BUV","target":"record","payload":{"canonical_record":{"source":{"id":"1407.7163","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DS","submitted_at":"2014-07-26T22:44:07Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"16308ee513e22a3ba4cad47e2c5ad20be231f6ae94588fe6659d1bb3f40a5271","abstract_canon_sha256":"b8e8ef1419b773a511679e37b6127f961f7275cbd3d3f9109e2452a792f76eb1"},"schema_version":"1.0"},"canonical_sha256":"dd44143277c0a1af9000324a5e03a1a540c43bb40cf411ace2923a525b0d8950","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:51.593302Z","signature_b64":"9jsRUfsc2xmDDYn8oFv2QJ8m3IZ+oRS6HrMUGuC4BGFyauZKNwSGIZZ229PAZCSNVO2pIWOHt3D2eteRQ3FIBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd44143277c0a1af9000324a5e03a1a540c43bb40cf411ace2923a525b0d8950","last_reissued_at":"2026-05-18T02:37:51.592675Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:51.592675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.7163","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":"2026-05-18T02:37:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wa2WFc3rLy2UCImKJVFWUWYDtnJEO5TsQp9mObJURoEgv/W+7YWulFuuI8hCz4uIDlduuI2PZa2sim0Cl8epDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:40:51.777471Z"},"content_sha256":"e5263a6ab325468544ef318d85252cbda7e4999e9da578c8e6cd858bfb0c7dcb","schema_version":"1.0","event_id":"sha256:e5263a6ab325468544ef318d85252cbda7e4999e9da578c8e6cd858bfb0c7dcb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3VCBIMTXYCQ27EAAGJFF4A5BUV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Who's Afraid of the Hill Boundary?","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.DS","authors_text":"Richard Montgomery","submitted_at":"2014-07-26T22:44:07Z","abstract_excerpt":"The Jacobi-Maupertuis metric allows one to reformulate Newton's equations as geodesic equations for a Riemannian metric which degenerates at the Hill boundary. We prove that a JM geodesic which comes sufficiently close to a regular point of the boundary contains pairs of conjugate points close to the boundary. We prove the conjugate locus of any point near enough to the boundary is a hypersurface tangent to the boundary. Our method of proof is to reduce analysis of geodesics near the boundary to that of solutions to Newton's equations in the simplest model case: a constant force. This model ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7163","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":"2026-05-18T02:37:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JxXqsfCzkWtlGY0rex5dOtFNEw3bM+ABRoAJHxHr5Jej9Cr9tq98AJFa2NH9GaIt012AkLfQGBjGApf9FpmoDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:40:51.777820Z"},"content_sha256":"deb2af58c776af4d73e71a63905ca75c59de50b629a221a82239d6f4b573a8da","schema_version":"1.0","event_id":"sha256:deb2af58c776af4d73e71a63905ca75c59de50b629a221a82239d6f4b573a8da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3VCBIMTXYCQ27EAAGJFF4A5BUV/bundle.json","state_url":"https://pith.science/pith/3VCBIMTXYCQ27EAAGJFF4A5BUV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3VCBIMTXYCQ27EAAGJFF4A5BUV/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":"2026-06-03T03:40:51Z","links":{"resolver":"https://pith.science/pith/3VCBIMTXYCQ27EAAGJFF4A5BUV","bundle":"https://pith.science/pith/3VCBIMTXYCQ27EAAGJFF4A5BUV/bundle.json","state":"https://pith.science/pith/3VCBIMTXYCQ27EAAGJFF4A5BUV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3VCBIMTXYCQ27EAAGJFF4A5BUV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3VCBIMTXYCQ27EAAGJFF4A5BUV","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":"b8e8ef1419b773a511679e37b6127f961f7275cbd3d3f9109e2452a792f76eb1","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DS","submitted_at":"2014-07-26T22:44:07Z","title_canon_sha256":"16308ee513e22a3ba4cad47e2c5ad20be231f6ae94588fe6659d1bb3f40a5271"},"schema_version":"1.0","source":{"id":"1407.7163","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.7163","created_at":"2026-05-18T02:37:51Z"},{"alias_kind":"arxiv_version","alias_value":"1407.7163v2","created_at":"2026-05-18T02:37:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7163","created_at":"2026-05-18T02:37:51Z"},{"alias_kind":"pith_short_12","alias_value":"3VCBIMTXYCQ2","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3VCBIMTXYCQ27EAA","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3VCBIMTX","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:deb2af58c776af4d73e71a63905ca75c59de50b629a221a82239d6f4b573a8da","target":"graph","created_at":"2026-05-18T02:37:51Z","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 Jacobi-Maupertuis metric allows one to reformulate Newton's equations as geodesic equations for a Riemannian metric which degenerates at the Hill boundary. We prove that a JM geodesic which comes sufficiently close to a regular point of the boundary contains pairs of conjugate points close to the boundary. We prove the conjugate locus of any point near enough to the boundary is a hypersurface tangent to the boundary. Our method of proof is to reduce analysis of geodesics near the boundary to that of solutions to Newton's equations in the simplest model case: a constant force. This model ca","authors_text":"Richard Montgomery","cross_cats":["math.DG"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DS","submitted_at":"2014-07-26T22:44:07Z","title":"Who's Afraid of the Hill Boundary?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7163","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:e5263a6ab325468544ef318d85252cbda7e4999e9da578c8e6cd858bfb0c7dcb","target":"record","created_at":"2026-05-18T02:37:51Z","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":"b8e8ef1419b773a511679e37b6127f961f7275cbd3d3f9109e2452a792f76eb1","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DS","submitted_at":"2014-07-26T22:44:07Z","title_canon_sha256":"16308ee513e22a3ba4cad47e2c5ad20be231f6ae94588fe6659d1bb3f40a5271"},"schema_version":"1.0","source":{"id":"1407.7163","kind":"arxiv","version":2}},"canonical_sha256":"dd44143277c0a1af9000324a5e03a1a540c43bb40cf411ace2923a525b0d8950","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd44143277c0a1af9000324a5e03a1a540c43bb40cf411ace2923a525b0d8950","first_computed_at":"2026-05-18T02:37:51.592675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:51.592675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9jsRUfsc2xmDDYn8oFv2QJ8m3IZ+oRS6HrMUGuC4BGFyauZKNwSGIZZ229PAZCSNVO2pIWOHt3D2eteRQ3FIBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:51.593302Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.7163","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5263a6ab325468544ef318d85252cbda7e4999e9da578c8e6cd858bfb0c7dcb","sha256:deb2af58c776af4d73e71a63905ca75c59de50b629a221a82239d6f4b573a8da"],"state_sha256":"198caf2d32b82f9cb8efe911ef651d8834cc32e80b666c27b66ad9be2e942603"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"42jgfo3StaFWfhV7Ta8xgyHT0V1aTlnc1XJjkKejnpMSbiSh1apx97/XZzizgyIsCfchkIzO9udX+rDvNtZ7Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T03:40:51.779768Z","bundle_sha256":"24fca050c8375d636d588e980c6abc5192c635135c583b12da3d699539c1947f"}}