{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1993:UKOSBTHBMZTJF7PKKH4FEWVEH2","short_pith_number":"pith:UKOSBTHB","canonical_record":{"source":{"id":"alg-geom/9303003","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1993-03-23T13:24:46Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c4ce21597f1e128041a83d02174f29ed8accfeab3b42959c273d99f1758e7f94","abstract_canon_sha256":"098967e623ffe751b0eb0fe1f499f06a990924cc98a439f9b69b3a1d31ff73e8"},"schema_version":"1.0"},"canonical_sha256":"a29d20cce1666692fdea51f8525aa43e96770461c4a3f52a914ab1fa8a039b3c","source":{"kind":"arxiv","id":"alg-geom/9303003","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9303003","created_at":"2026-05-18T01:37:43Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9303003v1","created_at":"2026-05-18T01:37:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9303003","created_at":"2026-05-18T01:37:43Z"},{"alias_kind":"pith_short_12","alias_value":"UKOSBTHBMZTJ","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"UKOSBTHBMZTJF7PK","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"UKOSBTHB","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1993:UKOSBTHBMZTJF7PKKH4FEWVEH2","target":"record","payload":{"canonical_record":{"source":{"id":"alg-geom/9303003","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1993-03-23T13:24:46Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c4ce21597f1e128041a83d02174f29ed8accfeab3b42959c273d99f1758e7f94","abstract_canon_sha256":"098967e623ffe751b0eb0fe1f499f06a990924cc98a439f9b69b3a1d31ff73e8"},"schema_version":"1.0"},"canonical_sha256":"a29d20cce1666692fdea51f8525aa43e96770461c4a3f52a914ab1fa8a039b3c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:43.186441Z","signature_b64":"ScBsnIvn0mPZA+xL7BiAIfPjXW8ORWh+bNQBwJycER5tkhSdtnPv1nvJLKLFAebwQm22KfyHX7cfbcPFAigHCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a29d20cce1666692fdea51f8525aa43e96770461c4a3f52a914ab1fa8a039b3c","last_reissued_at":"2026-05-18T01:37:43.185929Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:43.185929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"alg-geom/9303003","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":"2026-05-18T01:37:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eMp8+NOc368umCZdsrBSICQ6VVJNxaYyb/uOH7TL/no23WGQDvolt27riAaVtXx7U0o1DEmWPzWI5Pfj8rp4Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:11:34.229263Z"},"content_sha256":"0f0815e18b5bb12b264f2b2fa5a2e6e766fa3513b689b411725ff767a45330a5","schema_version":"1.0","event_id":"sha256:0f0815e18b5bb12b264f2b2fa5a2e6e766fa3513b689b411725ff767a45330a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1993:UKOSBTHBMZTJF7PKKH4FEWVEH2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deformations of cones over hyperelliptic curves","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Jan Stevens","submitted_at":"1993-03-23T13:24:46Z","abstract_excerpt":"We determine the versal deformation of cones, in the simplest case: cones over hyperelliptic curves of high degree. In particular, we show that for  degree $4g+4$, the highest degree for which interesting deformations exist, the number of smoothing components is $2^{2g+1}$ ($g\\neq3$).\n  We review in a general setting the relation of $T^1(-1)$ with Wahl's Gaussian map. We prove that $T^1(-1)$ vanishes for a general curve and an arbitrary embedding line bundle of degree at least $2g+11$. To find $T^2$ for hyperelliptic cones   with the Main Lemma of [Behnke--Christophersen], we compute  $T^1$ fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9303003","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":"2026-05-18T01:37:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A9f39LFuxvDgIA3FSO7dwt8rU/iQjkCOIy5E6owURNF48OzLqB87zVHHFZAHUyjPAaYP4d0yYljiUbmWWOoKCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:11:34.229611Z"},"content_sha256":"8bea2af086eef0a9408564734e20fd0b147b2c23076a67e39f57a095afec0a5e","schema_version":"1.0","event_id":"sha256:8bea2af086eef0a9408564734e20fd0b147b2c23076a67e39f57a095afec0a5e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UKOSBTHBMZTJF7PKKH4FEWVEH2/bundle.json","state_url":"https://pith.science/pith/UKOSBTHBMZTJF7PKKH4FEWVEH2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UKOSBTHBMZTJF7PKKH4FEWVEH2/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":"2026-06-06T20:11:34Z","links":{"resolver":"https://pith.science/pith/UKOSBTHBMZTJF7PKKH4FEWVEH2","bundle":"https://pith.science/pith/UKOSBTHBMZTJF7PKKH4FEWVEH2/bundle.json","state":"https://pith.science/pith/UKOSBTHBMZTJF7PKKH4FEWVEH2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UKOSBTHBMZTJF7PKKH4FEWVEH2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:UKOSBTHBMZTJF7PKKH4FEWVEH2","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":"098967e623ffe751b0eb0fe1f499f06a990924cc98a439f9b69b3a1d31ff73e8","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1993-03-23T13:24:46Z","title_canon_sha256":"c4ce21597f1e128041a83d02174f29ed8accfeab3b42959c273d99f1758e7f94"},"schema_version":"1.0","source":{"id":"alg-geom/9303003","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9303003","created_at":"2026-05-18T01:37:43Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9303003v1","created_at":"2026-05-18T01:37:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9303003","created_at":"2026-05-18T01:37:43Z"},{"alias_kind":"pith_short_12","alias_value":"UKOSBTHBMZTJ","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"UKOSBTHBMZTJF7PK","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"UKOSBTHB","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:8bea2af086eef0a9408564734e20fd0b147b2c23076a67e39f57a095afec0a5e","target":"graph","created_at":"2026-05-18T01:37:43Z","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 determine the versal deformation of cones, in the simplest case: cones over hyperelliptic curves of high degree. In particular, we show that for  degree $4g+4$, the highest degree for which interesting deformations exist, the number of smoothing components is $2^{2g+1}$ ($g\\neq3$).\n  We review in a general setting the relation of $T^1(-1)$ with Wahl's Gaussian map. We prove that $T^1(-1)$ vanishes for a general curve and an arbitrary embedding line bundle of degree at least $2g+11$. To find $T^2$ for hyperelliptic cones   with the Main Lemma of [Behnke--Christophersen], we compute  $T^1$ fo","authors_text":"Jan Stevens","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"alg-geom","submitted_at":"1993-03-23T13:24:46Z","title":"Deformations of cones over hyperelliptic curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9303003","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":"sha256:0f0815e18b5bb12b264f2b2fa5a2e6e766fa3513b689b411725ff767a45330a5","target":"record","created_at":"2026-05-18T01:37:43Z","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":"098967e623ffe751b0eb0fe1f499f06a990924cc98a439f9b69b3a1d31ff73e8","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1993-03-23T13:24:46Z","title_canon_sha256":"c4ce21597f1e128041a83d02174f29ed8accfeab3b42959c273d99f1758e7f94"},"schema_version":"1.0","source":{"id":"alg-geom/9303003","kind":"arxiv","version":1}},"canonical_sha256":"a29d20cce1666692fdea51f8525aa43e96770461c4a3f52a914ab1fa8a039b3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a29d20cce1666692fdea51f8525aa43e96770461c4a3f52a914ab1fa8a039b3c","first_computed_at":"2026-05-18T01:37:43.185929Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:43.185929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ScBsnIvn0mPZA+xL7BiAIfPjXW8ORWh+bNQBwJycER5tkhSdtnPv1nvJLKLFAebwQm22KfyHX7cfbcPFAigHCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:43.186441Z","signed_message":"canonical_sha256_bytes"},"source_id":"alg-geom/9303003","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f0815e18b5bb12b264f2b2fa5a2e6e766fa3513b689b411725ff767a45330a5","sha256:8bea2af086eef0a9408564734e20fd0b147b2c23076a67e39f57a095afec0a5e"],"state_sha256":"d30f11c519ec61cb6d089d1a70e290e2b2f06a3f9e857bd8e4ee8986ef4ff501"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rL1jG0341y99H/a3Zkv60IyDJn1jaLBCtHO67/B1vnFIwDz9E+iuXlTRwYIWBDbzXWvvBU9uwAO2Zmv+GRqDCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:11:34.231627Z","bundle_sha256":"760aef4de3194a59718f3b86679d0179a48559bf87a73dc176b9d69d62259b95"}}