{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JNBUZWWXACH5ID5FIM4RS6US3F","short_pith_number":"pith:JNBUZWWX","canonical_record":{"source":{"id":"1505.06945","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-26T13:44:22Z","cross_cats_sorted":[],"title_canon_sha256":"34c5024a0f5d2412ef5e5536bf3e32c1fbeee5a5b8e5fa546e327ce975cca136","abstract_canon_sha256":"3e12c1fb6a15ec3ec50b125126f0b7edc8543372ebf42fc18342fbc3f926888b"},"schema_version":"1.0"},"canonical_sha256":"4b434cdad7008fd40fa54339197a92d94ae01fa952f0bbd401ed842d49786f5e","source":{"kind":"arxiv","id":"1505.06945","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06945","created_at":"2026-05-18T02:03:27Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06945v1","created_at":"2026-05-18T02:03:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06945","created_at":"2026-05-18T02:03:27Z"},{"alias_kind":"pith_short_12","alias_value":"JNBUZWWXACH5","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JNBUZWWXACH5ID5F","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JNBUZWWX","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JNBUZWWXACH5ID5FIM4RS6US3F","target":"record","payload":{"canonical_record":{"source":{"id":"1505.06945","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-26T13:44:22Z","cross_cats_sorted":[],"title_canon_sha256":"34c5024a0f5d2412ef5e5536bf3e32c1fbeee5a5b8e5fa546e327ce975cca136","abstract_canon_sha256":"3e12c1fb6a15ec3ec50b125126f0b7edc8543372ebf42fc18342fbc3f926888b"},"schema_version":"1.0"},"canonical_sha256":"4b434cdad7008fd40fa54339197a92d94ae01fa952f0bbd401ed842d49786f5e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:27.481470Z","signature_b64":"Wc366PiX9YS/iUtAdIOcPgD4FjswWoxNo1dp42d0TnsaojML6HwO4eKVlG26X3fgSbP0BX9B45+JkeLZZSPJAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b434cdad7008fd40fa54339197a92d94ae01fa952f0bbd401ed842d49786f5e","last_reissued_at":"2026-05-18T02:03:27.480717Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:27.480717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.06945","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":"2026-05-18T02:03:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oUvyhfSeHef9YGlpBIXkQA9WboXOZafful5Dcm2OLFjFb6Qkyay3gm2xeVJSGOmxA9jO6s2Ajljd1NVxUZxuDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T07:00:32.831950Z"},"content_sha256":"cd6286ff5f7052c302650f3ed19506fccb7ce8d10605d30d4263c537f1cda4f2","schema_version":"1.0","event_id":"sha256:cd6286ff5f7052c302650f3ed19506fccb7ce8d10605d30d4263c537f1cda4f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JNBUZWWXACH5ID5FIM4RS6US3F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Differentiable distance spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"D. Cs. Kert\\'esz, L. Tam\\'assy","submitted_at":"2015-05-26T13:44:22Z","abstract_excerpt":"The distance function $\\varrho(p,q)$ (or $d(p,q)$) of a distance space (general metric space) is not differentiable in general. We investigate such distance spaces over $\\mathbb R^n$, whose distance functions are differentiable like in case of Finsler spaces. These spaces have several good properties, yet they are no Finsler spaces (which are special distance spaces). They are situated between general metric spaces (distance spaces) and Finsler spaces. We will investigate such curves of differentiable distance spaces, which possess the same properties as geodesics do in Finsler spaces. So thes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06945","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":"2026-05-18T02:03:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J13YM84aTj9k5hSmENJb+0nyCOTIRU3BZFT2KAs3JpaCFNBQiWicNLGLEv/a5D8x8ActCq2AhncOMcDvBN3+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T07:00:32.832511Z"},"content_sha256":"751feb63fc8092a7fbb3654120a0cbff6c6a9ded3b37de9d7fc13497c4a0fb4d","schema_version":"1.0","event_id":"sha256:751feb63fc8092a7fbb3654120a0cbff6c6a9ded3b37de9d7fc13497c4a0fb4d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JNBUZWWXACH5ID5FIM4RS6US3F/bundle.json","state_url":"https://pith.science/pith/JNBUZWWXACH5ID5FIM4RS6US3F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JNBUZWWXACH5ID5FIM4RS6US3F/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":"2026-06-30T07:00:32Z","links":{"resolver":"https://pith.science/pith/JNBUZWWXACH5ID5FIM4RS6US3F","bundle":"https://pith.science/pith/JNBUZWWXACH5ID5FIM4RS6US3F/bundle.json","state":"https://pith.science/pith/JNBUZWWXACH5ID5FIM4RS6US3F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JNBUZWWXACH5ID5FIM4RS6US3F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JNBUZWWXACH5ID5FIM4RS6US3F","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":"3e12c1fb6a15ec3ec50b125126f0b7edc8543372ebf42fc18342fbc3f926888b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-26T13:44:22Z","title_canon_sha256":"34c5024a0f5d2412ef5e5536bf3e32c1fbeee5a5b8e5fa546e327ce975cca136"},"schema_version":"1.0","source":{"id":"1505.06945","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06945","created_at":"2026-05-18T02:03:27Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06945v1","created_at":"2026-05-18T02:03:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06945","created_at":"2026-05-18T02:03:27Z"},{"alias_kind":"pith_short_12","alias_value":"JNBUZWWXACH5","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JNBUZWWXACH5ID5F","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JNBUZWWX","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:751feb63fc8092a7fbb3654120a0cbff6c6a9ded3b37de9d7fc13497c4a0fb4d","target":"graph","created_at":"2026-05-18T02:03:27Z","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 distance function $\\varrho(p,q)$ (or $d(p,q)$) of a distance space (general metric space) is not differentiable in general. We investigate such distance spaces over $\\mathbb R^n$, whose distance functions are differentiable like in case of Finsler spaces. These spaces have several good properties, yet they are no Finsler spaces (which are special distance spaces). They are situated between general metric spaces (distance spaces) and Finsler spaces. We will investigate such curves of differentiable distance spaces, which possess the same properties as geodesics do in Finsler spaces. So thes","authors_text":"D. Cs. Kert\\'esz, L. Tam\\'assy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-26T13:44:22Z","title":"Differentiable distance spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06945","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:cd6286ff5f7052c302650f3ed19506fccb7ce8d10605d30d4263c537f1cda4f2","target":"record","created_at":"2026-05-18T02:03:27Z","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":"3e12c1fb6a15ec3ec50b125126f0b7edc8543372ebf42fc18342fbc3f926888b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-26T13:44:22Z","title_canon_sha256":"34c5024a0f5d2412ef5e5536bf3e32c1fbeee5a5b8e5fa546e327ce975cca136"},"schema_version":"1.0","source":{"id":"1505.06945","kind":"arxiv","version":1}},"canonical_sha256":"4b434cdad7008fd40fa54339197a92d94ae01fa952f0bbd401ed842d49786f5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b434cdad7008fd40fa54339197a92d94ae01fa952f0bbd401ed842d49786f5e","first_computed_at":"2026-05-18T02:03:27.480717Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:27.480717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wc366PiX9YS/iUtAdIOcPgD4FjswWoxNo1dp42d0TnsaojML6HwO4eKVlG26X3fgSbP0BX9B45+JkeLZZSPJAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:27.481470Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.06945","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd6286ff5f7052c302650f3ed19506fccb7ce8d10605d30d4263c537f1cda4f2","sha256:751feb63fc8092a7fbb3654120a0cbff6c6a9ded3b37de9d7fc13497c4a0fb4d"],"state_sha256":"f5d083db076ceaac24362b7144390cbd7375c72cb422368a6cc25c6e7c9b6542"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y7/T5BF2ZUdSwbqbHiDgmX7lUraHnzbdmnaWn/FV2G9jfyvmHqO+a0RH4f6KFcCWrKA5APAK/WZ8epC73lyZAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T07:00:32.835190Z","bundle_sha256":"6057ad60afb1eb88b3f297502ac0d6c44fdb62140149403c55fb39c4742776fc"}}