{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:T33OOQPFGUBTDNQR5ZL424TIKH","short_pith_number":"pith:T33OOQPF","canonical_record":{"source":{"id":"1803.00981","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-02T18:21:37Z","cross_cats_sorted":[],"title_canon_sha256":"89ce3af8afe1c3135f7f17f69d395f3f016eadbdcd492dc62927467cfcc61a51","abstract_canon_sha256":"dda19dff10aab3e1d67869c2ebc45a825697872dbc83f331ad816773a7c09d8f"},"schema_version":"1.0"},"canonical_sha256":"9ef6e741e5350331b611ee57cd726851f052da2c638a69f6a655cb25a4fcabac","source":{"kind":"arxiv","id":"1803.00981","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00981","created_at":"2026-05-18T00:22:07Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00981v1","created_at":"2026-05-18T00:22:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00981","created_at":"2026-05-18T00:22:07Z"},{"alias_kind":"pith_short_12","alias_value":"T33OOQPFGUBT","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"T33OOQPFGUBTDNQR","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"T33OOQPF","created_at":"2026-05-18T12:32:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:T33OOQPFGUBTDNQR5ZL424TIKH","target":"record","payload":{"canonical_record":{"source":{"id":"1803.00981","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-02T18:21:37Z","cross_cats_sorted":[],"title_canon_sha256":"89ce3af8afe1c3135f7f17f69d395f3f016eadbdcd492dc62927467cfcc61a51","abstract_canon_sha256":"dda19dff10aab3e1d67869c2ebc45a825697872dbc83f331ad816773a7c09d8f"},"schema_version":"1.0"},"canonical_sha256":"9ef6e741e5350331b611ee57cd726851f052da2c638a69f6a655cb25a4fcabac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:07.335485Z","signature_b64":"i+Nldkrf0wutXBFUPwbl3glx9R9Ok0jQXn0U6kXUpwGhsX7v/QtlIBDMHDSlFutkNPlATojE1XM45/sOl4KPDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ef6e741e5350331b611ee57cd726851f052da2c638a69f6a655cb25a4fcabac","last_reissued_at":"2026-05-18T00:22:07.334784Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:07.334784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.00981","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":"2026-05-18T00:22:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NBMZllBfoZiGoj6gQSDVmP1h/dy/ne9H0tPM9dn41d6skcFOPIgRB4QJxAgX+slhwYQUVDa+u8CwFXdIItLlCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T17:49:39.725508Z"},"content_sha256":"111ef004b149ce491c98bc349ce6498831f1dcac41dd12022f0626311be38003","schema_version":"1.0","event_id":"sha256:111ef004b149ce491c98bc349ce6498831f1dcac41dd12022f0626311be38003"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:T33OOQPFGUBTDNQR5ZL424TIKH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On non-positive curvature properties of the Hilbert metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"L\\'aszl\\'o Kozma, Layth M. Alabdulsada","submitted_at":"2018-03-02T18:21:37Z","abstract_excerpt":"In this paper, we consider different types of non-positive curvature properties of the Hilbert metric of a convex domain in R^n. First, we survey the relationships among the concepts and prove that in the case of Hilbert metric some of them are equivalent. Furthermore, we show some condition which implies the rigidity feature: if the Hilbert metric is Berwald, i.e., its Finslerian Chern connection reduces to a linear one, then the domain is an ellipsoid and the metric is Riemannian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00981","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":"2026-05-18T00:22:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dgWZhij2WME7XZEKFtG03jPuAU6MzJe6ELZDPPyWowuK5QrpXasj88V5F0i0ebeObSwDKGm8vynDsU9LMksKCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T17:49:39.726131Z"},"content_sha256":"907801e7bd37827f56150f6b2b7e41141bd55585fbf81c2962c408b28fd0bc59","schema_version":"1.0","event_id":"sha256:907801e7bd37827f56150f6b2b7e41141bd55585fbf81c2962c408b28fd0bc59"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T33OOQPFGUBTDNQR5ZL424TIKH/bundle.json","state_url":"https://pith.science/pith/T33OOQPFGUBTDNQR5ZL424TIKH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T33OOQPFGUBTDNQR5ZL424TIKH/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":"2026-06-05T17:49:39Z","links":{"resolver":"https://pith.science/pith/T33OOQPFGUBTDNQR5ZL424TIKH","bundle":"https://pith.science/pith/T33OOQPFGUBTDNQR5ZL424TIKH/bundle.json","state":"https://pith.science/pith/T33OOQPFGUBTDNQR5ZL424TIKH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T33OOQPFGUBTDNQR5ZL424TIKH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:T33OOQPFGUBTDNQR5ZL424TIKH","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":"dda19dff10aab3e1d67869c2ebc45a825697872dbc83f331ad816773a7c09d8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-02T18:21:37Z","title_canon_sha256":"89ce3af8afe1c3135f7f17f69d395f3f016eadbdcd492dc62927467cfcc61a51"},"schema_version":"1.0","source":{"id":"1803.00981","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00981","created_at":"2026-05-18T00:22:07Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00981v1","created_at":"2026-05-18T00:22:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00981","created_at":"2026-05-18T00:22:07Z"},{"alias_kind":"pith_short_12","alias_value":"T33OOQPFGUBT","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"T33OOQPFGUBTDNQR","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"T33OOQPF","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:907801e7bd37827f56150f6b2b7e41141bd55585fbf81c2962c408b28fd0bc59","target":"graph","created_at":"2026-05-18T00:22:07Z","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":"In this paper, we consider different types of non-positive curvature properties of the Hilbert metric of a convex domain in R^n. First, we survey the relationships among the concepts and prove that in the case of Hilbert metric some of them are equivalent. Furthermore, we show some condition which implies the rigidity feature: if the Hilbert metric is Berwald, i.e., its Finslerian Chern connection reduces to a linear one, then the domain is an ellipsoid and the metric is Riemannian.","authors_text":"L\\'aszl\\'o Kozma, Layth M. Alabdulsada","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-02T18:21:37Z","title":"On non-positive curvature properties of the Hilbert metric"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00981","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":"sha256:111ef004b149ce491c98bc349ce6498831f1dcac41dd12022f0626311be38003","target":"record","created_at":"2026-05-18T00:22:07Z","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":"dda19dff10aab3e1d67869c2ebc45a825697872dbc83f331ad816773a7c09d8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-02T18:21:37Z","title_canon_sha256":"89ce3af8afe1c3135f7f17f69d395f3f016eadbdcd492dc62927467cfcc61a51"},"schema_version":"1.0","source":{"id":"1803.00981","kind":"arxiv","version":1}},"canonical_sha256":"9ef6e741e5350331b611ee57cd726851f052da2c638a69f6a655cb25a4fcabac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ef6e741e5350331b611ee57cd726851f052da2c638a69f6a655cb25a4fcabac","first_computed_at":"2026-05-18T00:22:07.334784Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:07.334784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i+Nldkrf0wutXBFUPwbl3glx9R9Ok0jQXn0U6kXUpwGhsX7v/QtlIBDMHDSlFutkNPlATojE1XM45/sOl4KPDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:07.335485Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.00981","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:111ef004b149ce491c98bc349ce6498831f1dcac41dd12022f0626311be38003","sha256:907801e7bd37827f56150f6b2b7e41141bd55585fbf81c2962c408b28fd0bc59"],"state_sha256":"0b34dba7dbdd5f8505183aaeef469146ce51be3f82bccaad6e795f1c683e69aa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RbY4aklqwbnq+ZlDZeqzmlee0ITknur089kg9IBRZf0NniNsmMzjhFGnzpygD99fJOa6cBn7F0nOtH6jkL0mDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T17:49:39.729220Z","bundle_sha256":"a09439778c4b90148e529f0643b97e1b1c0d21b01376ae5d2fdce072e618e8e8"}}