{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:KDRNWDHYJH6E2Z6KV52R65AUG7","short_pith_number":"pith:KDRNWDHY","canonical_record":{"source":{"id":"1706.06456","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-20T14:15:48Z","cross_cats_sorted":[],"title_canon_sha256":"865d4b667a4d2ee7b64774ed4de0c62a3193b30530322bc0ab0348f4015442dd","abstract_canon_sha256":"68978a6b0abd8b632c15cdf9e9558a895e75229eddff8da602f6c17ea89415de"},"schema_version":"1.0"},"canonical_sha256":"50e2db0cf849fc4d67caaf751f741437ed09723e547faf4849ac404aefb3cbb7","source":{"kind":"arxiv","id":"1706.06456","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.06456","created_at":"2026-07-04T23:52:31Z"},{"alias_kind":"arxiv_version","alias_value":"1706.06456v2","created_at":"2026-07-04T23:52:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06456","created_at":"2026-07-04T23:52:31Z"},{"alias_kind":"pith_short_12","alias_value":"KDRNWDHYJH6E","created_at":"2026-07-04T23:52:31Z"},{"alias_kind":"pith_short_16","alias_value":"KDRNWDHYJH6E2Z6K","created_at":"2026-07-04T23:52:31Z"},{"alias_kind":"pith_short_8","alias_value":"KDRNWDHY","created_at":"2026-07-04T23:52:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:KDRNWDHYJH6E2Z6KV52R65AUG7","target":"record","payload":{"canonical_record":{"source":{"id":"1706.06456","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-20T14:15:48Z","cross_cats_sorted":[],"title_canon_sha256":"865d4b667a4d2ee7b64774ed4de0c62a3193b30530322bc0ab0348f4015442dd","abstract_canon_sha256":"68978a6b0abd8b632c15cdf9e9558a895e75229eddff8da602f6c17ea89415de"},"schema_version":"1.0"},"canonical_sha256":"50e2db0cf849fc4d67caaf751f741437ed09723e547faf4849ac404aefb3cbb7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:52:31.564711Z","signature_b64":"t8Y4PoX7fnytHxQ7d5R4pZmuX9ic6FtYM1WzFhumermB83YSz58pwNnKeMfZ4Zp3Ktizk11CaQ4KyrVWC+MWDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50e2db0cf849fc4d67caaf751f741437ed09723e547faf4849ac404aefb3cbb7","last_reissued_at":"2026-07-04T23:52:31.564274Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:52:31.564274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.06456","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":"2026-07-04T23:52:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fzRiz6d73MR8OH//szrnkNitj+Q2+w5XE3/jL52kXLgDmkcG/SzGHXmO9eYO+0+SOhs7gsbFCneKa575HpJeDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T03:32:25.520104Z"},"content_sha256":"cc045be7b794d2dd03d315578f2c3a829609d4da014be2b87c43d91607fcecde","schema_version":"1.0","event_id":"sha256:cc045be7b794d2dd03d315578f2c3a829609d4da014be2b87c43d91607fcecde"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:KDRNWDHYJH6E2Z6KV52R65AUG7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eccentricities in the flip-graphs of convex polygons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lionel Pournin","submitted_at":"2017-06-20T14:15:48Z","abstract_excerpt":"The flip-graph of a convex polygon $\\pi$ is the graph whose vertices are the triangulations of $\\pi$ and whose edges correspond to flips between them. The eccentricity of a triangulation $T$ of $\\pi$ is the largest possible distance in this graph from $T$ to any triangulation of $\\pi$. It is well known that, when all $n-3$ interior edges of $T$ are incident to the same vertex, the eccentricity of $T$ in the flip-graph of $\\pi$ is exactly $n-3$, where $n$ denotes the number of vertices of $\\pi$. Here, this statement is generalized to arbitrary triangulations. Denoting by $n-3-k$ the largest num"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06456","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1706.06456/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T23:52:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v89xR6g1VWIeIqnjUOmsy3payD7vvSNPDqVECUrbNYUximRhrjOO9L09RAv6it7hrCu1mGWVH+UfX0ac0DTqCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T03:32:25.520479Z"},"content_sha256":"dbacdd47bde63cf0f65ef434b3a8f567cfe7b801c871de72d4b493277139b542","schema_version":"1.0","event_id":"sha256:dbacdd47bde63cf0f65ef434b3a8f567cfe7b801c871de72d4b493277139b542"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KDRNWDHYJH6E2Z6KV52R65AUG7/bundle.json","state_url":"https://pith.science/pith/KDRNWDHYJH6E2Z6KV52R65AUG7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KDRNWDHYJH6E2Z6KV52R65AUG7/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":"2026-08-04T03:32:25Z","links":{"resolver":"https://pith.science/pith/KDRNWDHYJH6E2Z6KV52R65AUG7","bundle":"https://pith.science/pith/KDRNWDHYJH6E2Z6KV52R65AUG7/bundle.json","state":"https://pith.science/pith/KDRNWDHYJH6E2Z6KV52R65AUG7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KDRNWDHYJH6E2Z6KV52R65AUG7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KDRNWDHYJH6E2Z6KV52R65AUG7","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":"68978a6b0abd8b632c15cdf9e9558a895e75229eddff8da602f6c17ea89415de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-20T14:15:48Z","title_canon_sha256":"865d4b667a4d2ee7b64774ed4de0c62a3193b30530322bc0ab0348f4015442dd"},"schema_version":"1.0","source":{"id":"1706.06456","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.06456","created_at":"2026-07-04T23:52:31Z"},{"alias_kind":"arxiv_version","alias_value":"1706.06456v2","created_at":"2026-07-04T23:52:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06456","created_at":"2026-07-04T23:52:31Z"},{"alias_kind":"pith_short_12","alias_value":"KDRNWDHYJH6E","created_at":"2026-07-04T23:52:31Z"},{"alias_kind":"pith_short_16","alias_value":"KDRNWDHYJH6E2Z6K","created_at":"2026-07-04T23:52:31Z"},{"alias_kind":"pith_short_8","alias_value":"KDRNWDHY","created_at":"2026-07-04T23:52:31Z"}],"graph_snapshots":[{"event_id":"sha256:dbacdd47bde63cf0f65ef434b3a8f567cfe7b801c871de72d4b493277139b542","target":"graph","created_at":"2026-07-04T23:52:31Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1706.06456/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The flip-graph of a convex polygon $\\pi$ is the graph whose vertices are the triangulations of $\\pi$ and whose edges correspond to flips between them. The eccentricity of a triangulation $T$ of $\\pi$ is the largest possible distance in this graph from $T$ to any triangulation of $\\pi$. It is well known that, when all $n-3$ interior edges of $T$ are incident to the same vertex, the eccentricity of $T$ in the flip-graph of $\\pi$ is exactly $n-3$, where $n$ denotes the number of vertices of $\\pi$. Here, this statement is generalized to arbitrary triangulations. Denoting by $n-3-k$ the largest num","authors_text":"Lionel Pournin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-20T14:15:48Z","title":"Eccentricities in the flip-graphs of convex polygons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06456","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:cc045be7b794d2dd03d315578f2c3a829609d4da014be2b87c43d91607fcecde","target":"record","created_at":"2026-07-04T23:52:31Z","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":"68978a6b0abd8b632c15cdf9e9558a895e75229eddff8da602f6c17ea89415de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-20T14:15:48Z","title_canon_sha256":"865d4b667a4d2ee7b64774ed4de0c62a3193b30530322bc0ab0348f4015442dd"},"schema_version":"1.0","source":{"id":"1706.06456","kind":"arxiv","version":2}},"canonical_sha256":"50e2db0cf849fc4d67caaf751f741437ed09723e547faf4849ac404aefb3cbb7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50e2db0cf849fc4d67caaf751f741437ed09723e547faf4849ac404aefb3cbb7","first_computed_at":"2026-07-04T23:52:31.564274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:52:31.564274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t8Y4PoX7fnytHxQ7d5R4pZmuX9ic6FtYM1WzFhumermB83YSz58pwNnKeMfZ4Zp3Ktizk11CaQ4KyrVWC+MWDg==","signature_status":"signed_v1","signed_at":"2026-07-04T23:52:31.564711Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.06456","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc045be7b794d2dd03d315578f2c3a829609d4da014be2b87c43d91607fcecde","sha256:dbacdd47bde63cf0f65ef434b3a8f567cfe7b801c871de72d4b493277139b542"],"state_sha256":"93f70aece88082cc4c3db16c32e299adb2edc6424a5cb4fddcb778abf9e0ba7b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b/iCcqC19KNW5HxKgUrNuFmbe2Ubr66VN+Efb2LFj47wk0Zt738FFjvjh58O9jB1Ld3fSS3LkwpoYu5QoEniAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T03:32:25.522784Z","bundle_sha256":"3a9b1180fc45cb0460192e334babe2ebce04663a9e0f1c92467b0490a009c215"}}