{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:33RGP5RN5ZXCZF4GACQRMG725G","short_pith_number":"pith:33RGP5RN","canonical_record":{"source":{"id":"2208.14409","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-08-30T17:20:30Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"15ca7da71dfc1eac3291373dbc28f40f81978c4d37ef35a2b809bb113429f7c2","abstract_canon_sha256":"da7ee6fa9fb130e850e8353955b28420b9f82efeb60fd1e91b0cbd46b3d18c4f"},"schema_version":"1.0"},"canonical_sha256":"dee267f62dee6e2c978600a1161bfae985e405b62f52ba4df747def9fd210983","source":{"kind":"arxiv","id":"2208.14409","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.14409","created_at":"2026-07-05T08:11:18Z"},{"alias_kind":"arxiv_version","alias_value":"2208.14409v2","created_at":"2026-07-05T08:11:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.14409","created_at":"2026-07-05T08:11:18Z"},{"alias_kind":"pith_short_12","alias_value":"33RGP5RN5ZXC","created_at":"2026-07-05T08:11:18Z"},{"alias_kind":"pith_short_16","alias_value":"33RGP5RN5ZXCZF4G","created_at":"2026-07-05T08:11:18Z"},{"alias_kind":"pith_short_8","alias_value":"33RGP5RN","created_at":"2026-07-05T08:11:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:33RGP5RN5ZXCZF4GACQRMG725G","target":"record","payload":{"canonical_record":{"source":{"id":"2208.14409","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-08-30T17:20:30Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"15ca7da71dfc1eac3291373dbc28f40f81978c4d37ef35a2b809bb113429f7c2","abstract_canon_sha256":"da7ee6fa9fb130e850e8353955b28420b9f82efeb60fd1e91b0cbd46b3d18c4f"},"schema_version":"1.0"},"canonical_sha256":"dee267f62dee6e2c978600a1161bfae985e405b62f52ba4df747def9fd210983","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:11:18.792685Z","signature_b64":"DoEHQggYOnJr2L5y4bfHu9QlUVQeri36SuIxi5mtaI21Irl6dxs8wvP4/FkDHP+jJ9iN+7n9ryvAOyMucDbgBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dee267f62dee6e2c978600a1161bfae985e405b62f52ba4df747def9fd210983","last_reissued_at":"2026-07-05T08:11:18.792239Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:11:18.792239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2208.14409","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":"2026-07-05T08:11:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PIzy4mTSZRD37XNjVkM5NJYGTUqjDe+WBRmdWdR4R6hc8TL1P1D3VB63hFbx+1gKm1NTjXliIRqw6rEayLghAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T00:28:55.894289Z"},"content_sha256":"c07fde8e8820967e5b99570c8a890adaed12193fbc484e83307a310ef146ae1f","schema_version":"1.0","event_id":"sha256:c07fde8e8820967e5b99570c8a890adaed12193fbc484e83307a310ef146ae1f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:33RGP5RN5ZXCZF4GACQRMG725G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial Almost-Complex Curves in $\\hat{\\mathbb{S}}^{2,4}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Parker Evans","submitted_at":"2022-08-30T17:20:30Z","abstract_excerpt":"For solutions to the $\\mathfrak{g}_2$ affine Toda field equations in $\\mathbb{C}$ with respect to \\emph{polynomial} holomorphic sextic differential $q$, we study the associated almost-complex curves $\\nu_q: \\mathbb{C} \\rightarrow \\hat{\\mathbb{S}}^{2,4}$. The asymptotic boundary $\\Delta := \\partial_{\\infty}(\\nu_q)$ of $\\nu_q$ is found to be a polygon in $\\mathsf{Ein}^{2,3}$ with $\\mathsf{deg} q + 6$ vertices. The polygon $\\Delta$ satisfies an \\emph{annihilator property}, which is related to a $\\mathsf{G}_2'$-invariant discrete metric $d_3: \\mathsf{Ein}^{2,3} \\times \\mathsf{Ein}^{2,3} \\rightarro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.14409","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/2208.14409/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":"2026-07-05T08:11:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h5QTioS+FsQgtImcAsqVRtFBYlOHeYe9RENJlmv19wVBmi3ut1LzUYK6tQXlRv5lOgCs4BFj5Jh/1XvjKVLnBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T00:28:55.894834Z"},"content_sha256":"8827dc9b90ba7a2b7b393b1c5fcf6f077071bffdd304920eaf10aebaa3f36ff2","schema_version":"1.0","event_id":"sha256:8827dc9b90ba7a2b7b393b1c5fcf6f077071bffdd304920eaf10aebaa3f36ff2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/33RGP5RN5ZXCZF4GACQRMG725G/bundle.json","state_url":"https://pith.science/pith/33RGP5RN5ZXCZF4GACQRMG725G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/33RGP5RN5ZXCZF4GACQRMG725G/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":"2026-08-10T00:28:55Z","links":{"resolver":"https://pith.science/pith/33RGP5RN5ZXCZF4GACQRMG725G","bundle":"https://pith.science/pith/33RGP5RN5ZXCZF4GACQRMG725G/bundle.json","state":"https://pith.science/pith/33RGP5RN5ZXCZF4GACQRMG725G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/33RGP5RN5ZXCZF4GACQRMG725G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:33RGP5RN5ZXCZF4GACQRMG725G","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":"da7ee6fa9fb130e850e8353955b28420b9f82efeb60fd1e91b0cbd46b3d18c4f","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-08-30T17:20:30Z","title_canon_sha256":"15ca7da71dfc1eac3291373dbc28f40f81978c4d37ef35a2b809bb113429f7c2"},"schema_version":"1.0","source":{"id":"2208.14409","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.14409","created_at":"2026-07-05T08:11:18Z"},{"alias_kind":"arxiv_version","alias_value":"2208.14409v2","created_at":"2026-07-05T08:11:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.14409","created_at":"2026-07-05T08:11:18Z"},{"alias_kind":"pith_short_12","alias_value":"33RGP5RN5ZXC","created_at":"2026-07-05T08:11:18Z"},{"alias_kind":"pith_short_16","alias_value":"33RGP5RN5ZXCZF4G","created_at":"2026-07-05T08:11:18Z"},{"alias_kind":"pith_short_8","alias_value":"33RGP5RN","created_at":"2026-07-05T08:11:18Z"}],"graph_snapshots":[{"event_id":"sha256:8827dc9b90ba7a2b7b393b1c5fcf6f077071bffdd304920eaf10aebaa3f36ff2","target":"graph","created_at":"2026-07-05T08:11:18Z","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/2208.14409/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For solutions to the $\\mathfrak{g}_2$ affine Toda field equations in $\\mathbb{C}$ with respect to \\emph{polynomial} holomorphic sextic differential $q$, we study the associated almost-complex curves $\\nu_q: \\mathbb{C} \\rightarrow \\hat{\\mathbb{S}}^{2,4}$. The asymptotic boundary $\\Delta := \\partial_{\\infty}(\\nu_q)$ of $\\nu_q$ is found to be a polygon in $\\mathsf{Ein}^{2,3}$ with $\\mathsf{deg} q + 6$ vertices. The polygon $\\Delta$ satisfies an \\emph{annihilator property}, which is related to a $\\mathsf{G}_2'$-invariant discrete metric $d_3: \\mathsf{Ein}^{2,3} \\times \\mathsf{Ein}^{2,3} \\rightarro","authors_text":"Parker Evans","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-08-30T17:20:30Z","title":"Polynomial Almost-Complex Curves in $\\hat{\\mathbb{S}}^{2,4}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.14409","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:c07fde8e8820967e5b99570c8a890adaed12193fbc484e83307a310ef146ae1f","target":"record","created_at":"2026-07-05T08:11:18Z","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":"da7ee6fa9fb130e850e8353955b28420b9f82efeb60fd1e91b0cbd46b3d18c4f","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-08-30T17:20:30Z","title_canon_sha256":"15ca7da71dfc1eac3291373dbc28f40f81978c4d37ef35a2b809bb113429f7c2"},"schema_version":"1.0","source":{"id":"2208.14409","kind":"arxiv","version":2}},"canonical_sha256":"dee267f62dee6e2c978600a1161bfae985e405b62f52ba4df747def9fd210983","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dee267f62dee6e2c978600a1161bfae985e405b62f52ba4df747def9fd210983","first_computed_at":"2026-07-05T08:11:18.792239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:11:18.792239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DoEHQggYOnJr2L5y4bfHu9QlUVQeri36SuIxi5mtaI21Irl6dxs8wvP4/FkDHP+jJ9iN+7n9ryvAOyMucDbgBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:11:18.792685Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.14409","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c07fde8e8820967e5b99570c8a890adaed12193fbc484e83307a310ef146ae1f","sha256:8827dc9b90ba7a2b7b393b1c5fcf6f077071bffdd304920eaf10aebaa3f36ff2"],"state_sha256":"c4274e087760c1874e1b61e6a9be02ade2f9117548f38369d4ab3024b6d4b339"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IBAhCaa8oFdVeYNVzkmJhSOfn0jTElTz/1isRDzEIrlkvasYAZOyl/+qd8gs8HIxS2jfra6Ws9xb3wk3ilI7DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T00:28:55.904764Z","bundle_sha256":"7706c0fe09827d128e3e97f8d45acbf66dd26a1539e1fc797ca5fc0359bbc9dd"}}