{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:VDMSSKKE22BUR4WFUQDKJXHPB5","short_pith_number":"pith:VDMSSKKE","canonical_record":{"source":{"id":"1602.06741","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-02-22T11:55:32Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"eb7e21aafea98909734569ce3d1f45316dea2e3b78c9eb90264910d738ef45bc","abstract_canon_sha256":"d2e6520693d5c0d45ed01db1043356934c2b28ced76159b59c32c2eeae5f8a0b"},"schema_version":"1.0"},"canonical_sha256":"a8d9292944d68348f2c5a406a4dcef0f732abe77eb5a13439baf333e37bff737","source":{"kind":"arxiv","id":"1602.06741","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.06741","created_at":"2026-05-18T00:27:04Z"},{"alias_kind":"arxiv_version","alias_value":"1602.06741v3","created_at":"2026-05-18T00:27:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.06741","created_at":"2026-05-18T00:27:04Z"},{"alias_kind":"pith_short_12","alias_value":"VDMSSKKE22BU","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VDMSSKKE22BUR4WF","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VDMSSKKE","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:VDMSSKKE22BUR4WFUQDKJXHPB5","target":"record","payload":{"canonical_record":{"source":{"id":"1602.06741","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-02-22T11:55:32Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"eb7e21aafea98909734569ce3d1f45316dea2e3b78c9eb90264910d738ef45bc","abstract_canon_sha256":"d2e6520693d5c0d45ed01db1043356934c2b28ced76159b59c32c2eeae5f8a0b"},"schema_version":"1.0"},"canonical_sha256":"a8d9292944d68348f2c5a406a4dcef0f732abe77eb5a13439baf333e37bff737","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:04.949710Z","signature_b64":"biq+82Y7Kqs4ioaoJnJw3uXUgznUCpsXxk2kqCR95AGFFx2AovVCSLnlFTBaMrCMjnD0IvO7e+901BVTlApOAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8d9292944d68348f2c5a406a4dcef0f732abe77eb5a13439baf333e37bff737","last_reissued_at":"2026-05-18T00:27:04.949064Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:04.949064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.06741","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:27:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ckTTLnhkqcXQR154ygmKsSVa9MuPW6G+o7QkAnN5jA9yH1Phdn4TsTRMLWLLyEuRKNyr2GAVWQ4CUXyIvcM4BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T01:51:08.447819Z"},"content_sha256":"e57acc70cc193b04d9d24b4ad012fc84de6a9949d07e4d4ab560f245813e3ae1","schema_version":"1.0","event_id":"sha256:e57acc70cc193b04d9d24b4ad012fc84de6a9949d07e4d4ab560f245813e3ae1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:VDMSSKKE22BUR4WFUQDKJXHPB5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal constants in normed planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Horst Martini, Ralph Teixeira, Vitor Balestro","submitted_at":"2016-02-22T11:55:32Z","abstract_excerpt":"We define new geometric constants for normed planes, determine their optimal values, and characterize types of planes for which these optimal values are attained. Relations of these constants to several topics, such as areas and distances from points to sides of triangles, are also investigated. We perform some calculations of new and old constants given by trigonometric functions for certain classes of norms, and a conjecture on vectors which are isosceles orthogonal is disproved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06741","kind":"arxiv","version":3},"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":"2026-05-18T00:27:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hv9SxobGUMCwm5QvGdzB8HdUsyyaqv7ZU7jfJ3ZQPhjW7/ww/2PuTOXIovtXwFm5IhmwnkDGW3P36u2s72YuBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T01:51:08.448161Z"},"content_sha256":"c62f5360b77eca83598b8003b1d28153f7e766e645740ba728ffbc9fa46bc884","schema_version":"1.0","event_id":"sha256:c62f5360b77eca83598b8003b1d28153f7e766e645740ba728ffbc9fa46bc884"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VDMSSKKE22BUR4WFUQDKJXHPB5/bundle.json","state_url":"https://pith.science/pith/VDMSSKKE22BUR4WFUQDKJXHPB5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VDMSSKKE22BUR4WFUQDKJXHPB5/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":"2026-06-24T01:51:08Z","links":{"resolver":"https://pith.science/pith/VDMSSKKE22BUR4WFUQDKJXHPB5","bundle":"https://pith.science/pith/VDMSSKKE22BUR4WFUQDKJXHPB5/bundle.json","state":"https://pith.science/pith/VDMSSKKE22BUR4WFUQDKJXHPB5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VDMSSKKE22BUR4WFUQDKJXHPB5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VDMSSKKE22BUR4WFUQDKJXHPB5","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":"d2e6520693d5c0d45ed01db1043356934c2b28ced76159b59c32c2eeae5f8a0b","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-02-22T11:55:32Z","title_canon_sha256":"eb7e21aafea98909734569ce3d1f45316dea2e3b78c9eb90264910d738ef45bc"},"schema_version":"1.0","source":{"id":"1602.06741","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.06741","created_at":"2026-05-18T00:27:04Z"},{"alias_kind":"arxiv_version","alias_value":"1602.06741v3","created_at":"2026-05-18T00:27:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.06741","created_at":"2026-05-18T00:27:04Z"},{"alias_kind":"pith_short_12","alias_value":"VDMSSKKE22BU","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VDMSSKKE22BUR4WF","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VDMSSKKE","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:c62f5360b77eca83598b8003b1d28153f7e766e645740ba728ffbc9fa46bc884","target":"graph","created_at":"2026-05-18T00:27:04Z","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 define new geometric constants for normed planes, determine their optimal values, and characterize types of planes for which these optimal values are attained. Relations of these constants to several topics, such as areas and distances from points to sides of triangles, are also investigated. We perform some calculations of new and old constants given by trigonometric functions for certain classes of norms, and a conjecture on vectors which are isosceles orthogonal is disproved.","authors_text":"Horst Martini, Ralph Teixeira, Vitor Balestro","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-02-22T11:55:32Z","title":"Optimal constants in normed planes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06741","kind":"arxiv","version":3},"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:e57acc70cc193b04d9d24b4ad012fc84de6a9949d07e4d4ab560f245813e3ae1","target":"record","created_at":"2026-05-18T00:27:04Z","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":"d2e6520693d5c0d45ed01db1043356934c2b28ced76159b59c32c2eeae5f8a0b","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-02-22T11:55:32Z","title_canon_sha256":"eb7e21aafea98909734569ce3d1f45316dea2e3b78c9eb90264910d738ef45bc"},"schema_version":"1.0","source":{"id":"1602.06741","kind":"arxiv","version":3}},"canonical_sha256":"a8d9292944d68348f2c5a406a4dcef0f732abe77eb5a13439baf333e37bff737","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8d9292944d68348f2c5a406a4dcef0f732abe77eb5a13439baf333e37bff737","first_computed_at":"2026-05-18T00:27:04.949064Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:04.949064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"biq+82Y7Kqs4ioaoJnJw3uXUgznUCpsXxk2kqCR95AGFFx2AovVCSLnlFTBaMrCMjnD0IvO7e+901BVTlApOAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:04.949710Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.06741","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e57acc70cc193b04d9d24b4ad012fc84de6a9949d07e4d4ab560f245813e3ae1","sha256:c62f5360b77eca83598b8003b1d28153f7e766e645740ba728ffbc9fa46bc884"],"state_sha256":"d05e892b96d8e6a0abd85f8eb20c7e59c450707c02b7fd8c1a721a8bc30e6e88"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/bJdEIJchraPUiWn1lLxdR7QP6E0lpVQ2Kw3x98fq7XV1KoaEVJLEbM/cAo8pivZ4nVUvfD4vsXCtLAjx2iaDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T01:51:08.450087Z","bundle_sha256":"58b577767be69b8c6ea2967715dcadaedb204fc284e279ac38a8fa7c80989462"}}