{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:UL2EA7PACW2MPLRLKWKYNC3VMU","short_pith_number":"pith:UL2EA7PA","canonical_record":{"source":{"id":"1908.04834","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-13T19:15:11Z","cross_cats_sorted":[],"title_canon_sha256":"478a30797c978e853cf82e996fd8bd2872b7e868aa4dd4d895f709347fbf2f8e","abstract_canon_sha256":"7baaf66ffab1e97e21ac0d97907b798793e76c5fa494597f68223f6f67172f63"},"schema_version":"1.0"},"canonical_sha256":"a2f4407de015b4c7ae2b5595868b75652800e5526affd79c73f81a0a7c64f185","source":{"kind":"arxiv","id":"1908.04834","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04834","created_at":"2026-07-05T05:06:48Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04834v2","created_at":"2026-07-05T05:06:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04834","created_at":"2026-07-05T05:06:48Z"},{"alias_kind":"pith_short_12","alias_value":"UL2EA7PACW2M","created_at":"2026-07-05T05:06:48Z"},{"alias_kind":"pith_short_16","alias_value":"UL2EA7PACW2MPLRL","created_at":"2026-07-05T05:06:48Z"},{"alias_kind":"pith_short_8","alias_value":"UL2EA7PA","created_at":"2026-07-05T05:06:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:UL2EA7PACW2MPLRLKWKYNC3VMU","target":"record","payload":{"canonical_record":{"source":{"id":"1908.04834","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-13T19:15:11Z","cross_cats_sorted":[],"title_canon_sha256":"478a30797c978e853cf82e996fd8bd2872b7e868aa4dd4d895f709347fbf2f8e","abstract_canon_sha256":"7baaf66ffab1e97e21ac0d97907b798793e76c5fa494597f68223f6f67172f63"},"schema_version":"1.0"},"canonical_sha256":"a2f4407de015b4c7ae2b5595868b75652800e5526affd79c73f81a0a7c64f185","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:06:48.493906Z","signature_b64":"pRhuRFVY6RPLP/whXTPEuIutzl68fWufMQIQY2/lPzz25SMCrGDGFXJceorRWcLN0J/DSvjYezI0mU+oxCqFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2f4407de015b4c7ae2b5595868b75652800e5526affd79c73f81a0a7c64f185","last_reissued_at":"2026-07-05T05:06:48.493575Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:06:48.493575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.04834","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":"2026-07-05T05:06:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mxVfhWAGYs6a7EIxcYo9fyfWDHtyWiCiWR8LZ12SAEf8jKGGXmF03+juV5VJtV2nJXwQ8covgjMKbNkQ8s2IBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:36:03.278193Z"},"content_sha256":"6d7a8c40f162ff589b60447878e9e7f543767e449987d3c28bfd8df27bfa4dfd","schema_version":"1.0","event_id":"sha256:6d7a8c40f162ff589b60447878e9e7f543767e449987d3c28bfd8df27bfa4dfd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:UL2EA7PACW2MPLRLKWKYNC3VMU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the asymptotic geometry of finite-type $k$-surfaces in three-dimensional hyperbolic space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Graham Smith","submitted_at":"2019-08-13T19:15:11Z","abstract_excerpt":"For $0<k<1$, a finite-type $k$-surface in $3$-dimensional hyperbolic space is a complete, immersed surface of finite area and of constant extrinsic curvature equal to $k$. In [32], we showed that such surfaces have finite genus and finitely many cusp-like ends. Each of these cusps is asymptotic to an immersed cylinder of exponentially decaying radius about a complete geodesic and terminates at an ideal point which we call the extremity of the cusp. We show that every cusp of any finite-type $k$-surface has a well-defined axis, which we will call the Steiner geodesic of the cusp. One of its end"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04834","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/1908.04834/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":"2026-07-05T05:06:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5l5+rMS9vCguiycBCrP874gMVOML6sAgaWWMhJMEQxt3KgHrm9KSImMBhjCFDM07r1WzqMoYrgQ10KeNy9HTBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:36:03.279112Z"},"content_sha256":"00d7f4bfd7d5803872852fa58d8be8f9a13af3a825c420db02a8236ca695dcf8","schema_version":"1.0","event_id":"sha256:00d7f4bfd7d5803872852fa58d8be8f9a13af3a825c420db02a8236ca695dcf8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UL2EA7PACW2MPLRLKWKYNC3VMU/bundle.json","state_url":"https://pith.science/pith/UL2EA7PACW2MPLRLKWKYNC3VMU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UL2EA7PACW2MPLRLKWKYNC3VMU/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":"2026-08-16T15:36:03Z","links":{"resolver":"https://pith.science/pith/UL2EA7PACW2MPLRLKWKYNC3VMU","bundle":"https://pith.science/pith/UL2EA7PACW2MPLRLKWKYNC3VMU/bundle.json","state":"https://pith.science/pith/UL2EA7PACW2MPLRLKWKYNC3VMU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UL2EA7PACW2MPLRLKWKYNC3VMU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:UL2EA7PACW2MPLRLKWKYNC3VMU","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":"7baaf66ffab1e97e21ac0d97907b798793e76c5fa494597f68223f6f67172f63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-13T19:15:11Z","title_canon_sha256":"478a30797c978e853cf82e996fd8bd2872b7e868aa4dd4d895f709347fbf2f8e"},"schema_version":"1.0","source":{"id":"1908.04834","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.04834","created_at":"2026-07-05T05:06:48Z"},{"alias_kind":"arxiv_version","alias_value":"1908.04834v2","created_at":"2026-07-05T05:06:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.04834","created_at":"2026-07-05T05:06:48Z"},{"alias_kind":"pith_short_12","alias_value":"UL2EA7PACW2M","created_at":"2026-07-05T05:06:48Z"},{"alias_kind":"pith_short_16","alias_value":"UL2EA7PACW2MPLRL","created_at":"2026-07-05T05:06:48Z"},{"alias_kind":"pith_short_8","alias_value":"UL2EA7PA","created_at":"2026-07-05T05:06:48Z"}],"graph_snapshots":[{"event_id":"sha256:00d7f4bfd7d5803872852fa58d8be8f9a13af3a825c420db02a8236ca695dcf8","target":"graph","created_at":"2026-07-05T05:06:48Z","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/1908.04834/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For $0<k<1$, a finite-type $k$-surface in $3$-dimensional hyperbolic space is a complete, immersed surface of finite area and of constant extrinsic curvature equal to $k$. In [32], we showed that such surfaces have finite genus and finitely many cusp-like ends. Each of these cusps is asymptotic to an immersed cylinder of exponentially decaying radius about a complete geodesic and terminates at an ideal point which we call the extremity of the cusp. We show that every cusp of any finite-type $k$-surface has a well-defined axis, which we will call the Steiner geodesic of the cusp. One of its end","authors_text":"Graham Smith","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-13T19:15:11Z","title":"On the asymptotic geometry of finite-type $k$-surfaces in three-dimensional hyperbolic space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04834","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":"sha256:6d7a8c40f162ff589b60447878e9e7f543767e449987d3c28bfd8df27bfa4dfd","target":"record","created_at":"2026-07-05T05:06:48Z","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":"7baaf66ffab1e97e21ac0d97907b798793e76c5fa494597f68223f6f67172f63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-13T19:15:11Z","title_canon_sha256":"478a30797c978e853cf82e996fd8bd2872b7e868aa4dd4d895f709347fbf2f8e"},"schema_version":"1.0","source":{"id":"1908.04834","kind":"arxiv","version":2}},"canonical_sha256":"a2f4407de015b4c7ae2b5595868b75652800e5526affd79c73f81a0a7c64f185","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2f4407de015b4c7ae2b5595868b75652800e5526affd79c73f81a0a7c64f185","first_computed_at":"2026-07-05T05:06:48.493575Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:06:48.493575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pRhuRFVY6RPLP/whXTPEuIutzl68fWufMQIQY2/lPzz25SMCrGDGFXJceorRWcLN0J/DSvjYezI0mU+oxCqFCw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:06:48.493906Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.04834","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d7a8c40f162ff589b60447878e9e7f543767e449987d3c28bfd8df27bfa4dfd","sha256:00d7f4bfd7d5803872852fa58d8be8f9a13af3a825c420db02a8236ca695dcf8"],"state_sha256":"0dd3118f4a88b5784a4c160839c6ddd0b6a17b2238b205b251579f8a77143427"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K98jzREk9JWvUgYdXrtqzoPuobbwSjzalK/1QoHdLhqe9awTa5EUlf05vOyv20fahsnX51SoeS4+BW5n/QHvCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T15:36:03.364618Z","bundle_sha256":"8424e9954f5c4618dd36fe3032dd7afad7db51e519e00d347aff08895d225119"}}