{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:NKKJTKL5VWPR7XMIWVQ3BSBCOY","short_pith_number":"pith:NKKJTKL5","canonical_record":{"source":{"id":"2506.12465","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-06-14T12:05:29Z","cross_cats_sorted":[],"title_canon_sha256":"c588c4cc72652d33abb43edb38361040122fdfeace53d5161fec4fca10a35e45","abstract_canon_sha256":"c2a895b192425f4bc16a871895b7ca4fe28064d5782ef879baae0f15cb372519"},"schema_version":"1.0"},"canonical_sha256":"6a9499a97dad9f1fdd88b561b0c82276021e93866165e35b381085e0b919cbae","source":{"kind":"arxiv","id":"2506.12465","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.12465","created_at":"2026-07-05T11:21:53Z"},{"alias_kind":"arxiv_version","alias_value":"2506.12465v1","created_at":"2026-07-05T11:21:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.12465","created_at":"2026-07-05T11:21:53Z"},{"alias_kind":"pith_short_12","alias_value":"NKKJTKL5VWPR","created_at":"2026-07-05T11:21:53Z"},{"alias_kind":"pith_short_16","alias_value":"NKKJTKL5VWPR7XMI","created_at":"2026-07-05T11:21:53Z"},{"alias_kind":"pith_short_8","alias_value":"NKKJTKL5","created_at":"2026-07-05T11:21:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:NKKJTKL5VWPR7XMIWVQ3BSBCOY","target":"record","payload":{"canonical_record":{"source":{"id":"2506.12465","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-06-14T12:05:29Z","cross_cats_sorted":[],"title_canon_sha256":"c588c4cc72652d33abb43edb38361040122fdfeace53d5161fec4fca10a35e45","abstract_canon_sha256":"c2a895b192425f4bc16a871895b7ca4fe28064d5782ef879baae0f15cb372519"},"schema_version":"1.0"},"canonical_sha256":"6a9499a97dad9f1fdd88b561b0c82276021e93866165e35b381085e0b919cbae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:21:53.809550Z","signature_b64":"ABrB0KMIg7jxrbWpTRsZiyIec/5ZqdIbN6uzjXCDqpIeUlXK0Ckl4L/PVrVd4jrf4fTioucbOzFin7tM4niwBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a9499a97dad9f1fdd88b561b0c82276021e93866165e35b381085e0b919cbae","last_reissued_at":"2026-07-05T11:21:53.809099Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:21:53.809099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.12465","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":"2026-07-05T11:21:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jo3/qJaSHkFqQiuObGYZlKnmnYvTmvl8E2eKEappAxQTPCltTkkWaScT/Gbr5jai9mrdCakP3LiIe1tX8rSGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:24:33.685355Z"},"content_sha256":"782a8f22aea4c88d651597259d46c1e71bba3fa19b8f13ea1421205a8b00613c","schema_version":"1.0","event_id":"sha256:782a8f22aea4c88d651597259d46c1e71bba3fa19b8f13ea1421205a8b00613c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:NKKJTKL5VWPR7XMIWVQ3BSBCOY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Shortest filling geodesics on hyperbolic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Jiajun Wang, Yue Gao, Zhongzi Wang","submitted_at":"2025-06-14T12:05:29Z","abstract_excerpt":"In this paper, we obtain the minimal length of a filling (multi-)geodesic on a genus $g$ hyperbolic surface in the moduli space of hyperbolic surfaces and show that it is realized by the geodesic whose complement is a right-angled regular $(8g-4)$-gon. A single geodesic realizing this minimum is provided."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.12465","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.12465/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":"2026-07-05T11:21:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XKYJLt25dVBCg4GG3g4ZRQ+qHGeSZkFXidqGoYSAgyIVAZ4OWP1Mcx/32QjyJE7qtCuJp8VuO5jf5gOJHwo9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:24:33.686019Z"},"content_sha256":"3f096f60499d1e0f5679bf692a3b27d4ed6c03ad1b542a4e1d11329187971470","schema_version":"1.0","event_id":"sha256:3f096f60499d1e0f5679bf692a3b27d4ed6c03ad1b542a4e1d11329187971470"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NKKJTKL5VWPR7XMIWVQ3BSBCOY/bundle.json","state_url":"https://pith.science/pith/NKKJTKL5VWPR7XMIWVQ3BSBCOY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NKKJTKL5VWPR7XMIWVQ3BSBCOY/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":"2026-08-12T22:24:33Z","links":{"resolver":"https://pith.science/pith/NKKJTKL5VWPR7XMIWVQ3BSBCOY","bundle":"https://pith.science/pith/NKKJTKL5VWPR7XMIWVQ3BSBCOY/bundle.json","state":"https://pith.science/pith/NKKJTKL5VWPR7XMIWVQ3BSBCOY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NKKJTKL5VWPR7XMIWVQ3BSBCOY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:NKKJTKL5VWPR7XMIWVQ3BSBCOY","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":"c2a895b192425f4bc16a871895b7ca4fe28064d5782ef879baae0f15cb372519","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-06-14T12:05:29Z","title_canon_sha256":"c588c4cc72652d33abb43edb38361040122fdfeace53d5161fec4fca10a35e45"},"schema_version":"1.0","source":{"id":"2506.12465","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.12465","created_at":"2026-07-05T11:21:53Z"},{"alias_kind":"arxiv_version","alias_value":"2506.12465v1","created_at":"2026-07-05T11:21:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.12465","created_at":"2026-07-05T11:21:53Z"},{"alias_kind":"pith_short_12","alias_value":"NKKJTKL5VWPR","created_at":"2026-07-05T11:21:53Z"},{"alias_kind":"pith_short_16","alias_value":"NKKJTKL5VWPR7XMI","created_at":"2026-07-05T11:21:53Z"},{"alias_kind":"pith_short_8","alias_value":"NKKJTKL5","created_at":"2026-07-05T11:21:53Z"}],"graph_snapshots":[{"event_id":"sha256:3f096f60499d1e0f5679bf692a3b27d4ed6c03ad1b542a4e1d11329187971470","target":"graph","created_at":"2026-07-05T11:21:53Z","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/2506.12465/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we obtain the minimal length of a filling (multi-)geodesic on a genus $g$ hyperbolic surface in the moduli space of hyperbolic surfaces and show that it is realized by the geodesic whose complement is a right-angled regular $(8g-4)$-gon. A single geodesic realizing this minimum is provided.","authors_text":"Jiajun Wang, Yue Gao, Zhongzi Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-06-14T12:05:29Z","title":"Shortest filling geodesics on hyperbolic surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.12465","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":"sha256:782a8f22aea4c88d651597259d46c1e71bba3fa19b8f13ea1421205a8b00613c","target":"record","created_at":"2026-07-05T11:21:53Z","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":"c2a895b192425f4bc16a871895b7ca4fe28064d5782ef879baae0f15cb372519","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-06-14T12:05:29Z","title_canon_sha256":"c588c4cc72652d33abb43edb38361040122fdfeace53d5161fec4fca10a35e45"},"schema_version":"1.0","source":{"id":"2506.12465","kind":"arxiv","version":1}},"canonical_sha256":"6a9499a97dad9f1fdd88b561b0c82276021e93866165e35b381085e0b919cbae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a9499a97dad9f1fdd88b561b0c82276021e93866165e35b381085e0b919cbae","first_computed_at":"2026-07-05T11:21:53.809099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:21:53.809099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ABrB0KMIg7jxrbWpTRsZiyIec/5ZqdIbN6uzjXCDqpIeUlXK0Ckl4L/PVrVd4jrf4fTioucbOzFin7tM4niwBA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:21:53.809550Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.12465","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:782a8f22aea4c88d651597259d46c1e71bba3fa19b8f13ea1421205a8b00613c","sha256:3f096f60499d1e0f5679bf692a3b27d4ed6c03ad1b542a4e1d11329187971470"],"state_sha256":"3454420f86fba256219b7d37d54ca6ab0880c36a992eaa401bfe8f5a8557b449"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"unYgLwTPtMHVHUcpsmWZ4sL4MZppFxAm1xRcLwcQJTcxUITEDIhE3zgrTF/zzm7rzSB6sepQzTjqSDUZONjiAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T22:24:33.691257Z","bundle_sha256":"0bb2c49547d5e8cacbdb704158988ecdf619928b853cc06dded819de730cdba5"}}