{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:HJT5HOLUU3TVO42NYSTMGLW32M","short_pith_number":"pith:HJT5HOLU","canonical_record":{"source":{"id":"math/0608224","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2006-08-09T14:37:45Z","cross_cats_sorted":[],"title_canon_sha256":"41733b903d00202312c0d34f2d8f5490ff02bdc1a5536adeda5402b05c33d6df","abstract_canon_sha256":"90642aa8cbe0414aa3cfdfcee53c3ae95186c03c76432aed4f96f52eac496418"},"schema_version":"1.0"},"canonical_sha256":"3a67d3b974a6e757734dc4a6c32edbd32dee578576a25d46d39e1b48bf693885","source":{"kind":"arxiv","id":"math/0608224","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0608224","created_at":"2026-07-04T14:56:05Z"},{"alias_kind":"arxiv_version","alias_value":"math/0608224v2","created_at":"2026-07-04T14:56:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0608224","created_at":"2026-07-04T14:56:05Z"},{"alias_kind":"pith_short_12","alias_value":"HJT5HOLUU3TV","created_at":"2026-07-04T14:56:05Z"},{"alias_kind":"pith_short_16","alias_value":"HJT5HOLUU3TVO42N","created_at":"2026-07-04T14:56:05Z"},{"alias_kind":"pith_short_8","alias_value":"HJT5HOLU","created_at":"2026-07-04T14:56:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:HJT5HOLUU3TVO42NYSTMGLW32M","target":"record","payload":{"canonical_record":{"source":{"id":"math/0608224","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2006-08-09T14:37:45Z","cross_cats_sorted":[],"title_canon_sha256":"41733b903d00202312c0d34f2d8f5490ff02bdc1a5536adeda5402b05c33d6df","abstract_canon_sha256":"90642aa8cbe0414aa3cfdfcee53c3ae95186c03c76432aed4f96f52eac496418"},"schema_version":"1.0"},"canonical_sha256":"3a67d3b974a6e757734dc4a6c32edbd32dee578576a25d46d39e1b48bf693885","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:56:05.822642Z","signature_b64":"IvtmVI6sp5Ht5Bn+oKQZgUagW9awfaNcbF10gZAn0OfCvQQlHPWmou4b0G/KVJzAnGSqODl2kIe9Zv0Rk/RZAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a67d3b974a6e757734dc4a6c32edbd32dee578576a25d46d39e1b48bf693885","last_reissued_at":"2026-07-04T14:56:05.822209Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:56:05.822209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0608224","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":"2026-07-04T14:56:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fpA0oerfPuWrpLju8MielLkPYBMWdoVFZ85yi0o8bvYQE9OTLHRX686w7o/5XneAxK6Qdu8a4/nsSlT1LhRBDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T08:43:29.794357Z"},"content_sha256":"72c0cfd1612bc3b0a7887bffd25017352f124054a4420e34f08a54ec6cbf0ae4","schema_version":"1.0","event_id":"sha256:72c0cfd1612bc3b0a7887bffd25017352f124054a4420e34f08a54ec6cbf0ae4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:HJT5HOLUU3TVO42NYSTMGLW32M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Seshadri constants on symmetric products of curves","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"J. Ross","submitted_at":"2006-08-09T14:37:45Z","abstract_excerpt":"Let X_g=C^{(2)}_g be the second symmetric product of a very general curve of genus g. We reduce the problem of describing the ample cone on X_g to a problem involving the Seshadri constant of a point on X_{g-1}. Using this we recover a result of Ciliberto-Kouvidakis that reduces finding the ample cone of X_g to the Nagata conjecture when g\\ge 9. We also give new bounds on the the ample cone of X_g when g=5."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608224","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/math/0608224/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":"2026-07-04T14:56:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EI38lu21QiyxrUS4lR20TMpTcH6/OTqiqjMMDwgoXPBmz1Qi7/NaVPyJKkSJd8THRlwVSSdbvUlEUWnpxi5ADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T08:43:29.794909Z"},"content_sha256":"6468e100e4d821d5823f94cf56096c8b9ef409c7bcc2e1c9d08fa33cebd625b4","schema_version":"1.0","event_id":"sha256:6468e100e4d821d5823f94cf56096c8b9ef409c7bcc2e1c9d08fa33cebd625b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HJT5HOLUU3TVO42NYSTMGLW32M/bundle.json","state_url":"https://pith.science/pith/HJT5HOLUU3TVO42NYSTMGLW32M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HJT5HOLUU3TVO42NYSTMGLW32M/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":"2026-08-01T08:43:29Z","links":{"resolver":"https://pith.science/pith/HJT5HOLUU3TVO42NYSTMGLW32M","bundle":"https://pith.science/pith/HJT5HOLUU3TVO42NYSTMGLW32M/bundle.json","state":"https://pith.science/pith/HJT5HOLUU3TVO42NYSTMGLW32M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HJT5HOLUU3TVO42NYSTMGLW32M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:HJT5HOLUU3TVO42NYSTMGLW32M","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":"90642aa8cbe0414aa3cfdfcee53c3ae95186c03c76432aed4f96f52eac496418","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2006-08-09T14:37:45Z","title_canon_sha256":"41733b903d00202312c0d34f2d8f5490ff02bdc1a5536adeda5402b05c33d6df"},"schema_version":"1.0","source":{"id":"math/0608224","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0608224","created_at":"2026-07-04T14:56:05Z"},{"alias_kind":"arxiv_version","alias_value":"math/0608224v2","created_at":"2026-07-04T14:56:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0608224","created_at":"2026-07-04T14:56:05Z"},{"alias_kind":"pith_short_12","alias_value":"HJT5HOLUU3TV","created_at":"2026-07-04T14:56:05Z"},{"alias_kind":"pith_short_16","alias_value":"HJT5HOLUU3TVO42N","created_at":"2026-07-04T14:56:05Z"},{"alias_kind":"pith_short_8","alias_value":"HJT5HOLU","created_at":"2026-07-04T14:56:05Z"}],"graph_snapshots":[{"event_id":"sha256:6468e100e4d821d5823f94cf56096c8b9ef409c7bcc2e1c9d08fa33cebd625b4","target":"graph","created_at":"2026-07-04T14:56:05Z","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/math/0608224/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let X_g=C^{(2)}_g be the second symmetric product of a very general curve of genus g. We reduce the problem of describing the ample cone on X_g to a problem involving the Seshadri constant of a point on X_{g-1}. Using this we recover a result of Ciliberto-Kouvidakis that reduces finding the ample cone of X_g to the Nagata conjecture when g\\ge 9. We also give new bounds on the the ample cone of X_g when g=5.","authors_text":"J. Ross","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2006-08-09T14:37:45Z","title":"Seshadri constants on symmetric products of curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608224","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":"sha256:72c0cfd1612bc3b0a7887bffd25017352f124054a4420e34f08a54ec6cbf0ae4","target":"record","created_at":"2026-07-04T14:56:05Z","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":"90642aa8cbe0414aa3cfdfcee53c3ae95186c03c76432aed4f96f52eac496418","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2006-08-09T14:37:45Z","title_canon_sha256":"41733b903d00202312c0d34f2d8f5490ff02bdc1a5536adeda5402b05c33d6df"},"schema_version":"1.0","source":{"id":"math/0608224","kind":"arxiv","version":2}},"canonical_sha256":"3a67d3b974a6e757734dc4a6c32edbd32dee578576a25d46d39e1b48bf693885","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a67d3b974a6e757734dc4a6c32edbd32dee578576a25d46d39e1b48bf693885","first_computed_at":"2026-07-04T14:56:05.822209Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:56:05.822209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IvtmVI6sp5Ht5Bn+oKQZgUagW9awfaNcbF10gZAn0OfCvQQlHPWmou4b0G/KVJzAnGSqODl2kIe9Zv0Rk/RZAQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:56:05.822642Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0608224","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72c0cfd1612bc3b0a7887bffd25017352f124054a4420e34f08a54ec6cbf0ae4","sha256:6468e100e4d821d5823f94cf56096c8b9ef409c7bcc2e1c9d08fa33cebd625b4"],"state_sha256":"98198b0408e4482f44b88e56633a4e61e50be884e7431149630a8a0cd71f4ca1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I9/Jc7dbp0de61j2/rXJIo8TzUMF4XrSl6dnf/q0yBwWJhBo/9l9wz8NvQ380wkDoqYyQbRDL2H3In7RgQ6rCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-01T08:43:29.800232Z","bundle_sha256":"cea7ac12923884535f93e17760f36e7245300d925874169bd135f66fad1e7203"}}