{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:DPU5ET5HIWDONDGY5X25UHBMMA","short_pith_number":"pith:DPU5ET5H","canonical_record":{"source":{"id":"1204.3161","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-14T10:36:28Z","cross_cats_sorted":[],"title_canon_sha256":"64570e1b65a2e2e68bd83bfbebd17513643d48743ee78584f13b0e7a4f0ab41e","abstract_canon_sha256":"171bc5b94ec3ba302290baf60170ff08a03ff5107f52037578a1677b2b3df3d6"},"schema_version":"1.0"},"canonical_sha256":"1be9d24fa74586e68cd8edf5da1c2c602cdc7f81c7a10d9186dcebbdd69ffdaa","source":{"kind":"arxiv","id":"1204.3161","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3161","created_at":"2026-05-18T03:57:52Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3161v1","created_at":"2026-05-18T03:57:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3161","created_at":"2026-05-18T03:57:52Z"},{"alias_kind":"pith_short_12","alias_value":"DPU5ET5HIWDO","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DPU5ET5HIWDONDGY","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DPU5ET5H","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:DPU5ET5HIWDONDGY5X25UHBMMA","target":"record","payload":{"canonical_record":{"source":{"id":"1204.3161","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-14T10:36:28Z","cross_cats_sorted":[],"title_canon_sha256":"64570e1b65a2e2e68bd83bfbebd17513643d48743ee78584f13b0e7a4f0ab41e","abstract_canon_sha256":"171bc5b94ec3ba302290baf60170ff08a03ff5107f52037578a1677b2b3df3d6"},"schema_version":"1.0"},"canonical_sha256":"1be9d24fa74586e68cd8edf5da1c2c602cdc7f81c7a10d9186dcebbdd69ffdaa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:52.421455Z","signature_b64":"R9gUqCkfyFq6qD/3RFkjvcGe2zuUIOeUQBf5FwGBTziyWoywOljbcmQY20ZEuwjz2qR6SWLh4MYCKIC/xL8aBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1be9d24fa74586e68cd8edf5da1c2c602cdc7f81c7a10d9186dcebbdd69ffdaa","last_reissued_at":"2026-05-18T03:57:52.420698Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:52.420698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.3161","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":"2026-05-18T03:57:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lmw3oUB1nvfRbtwmWQmPfE/O4Xncc8YrQQIEBgL00bqSIgNRczvn18X8fISk3bAadNOXvTR5xCNPAKuFUreYAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:07:43.008651Z"},"content_sha256":"e442559fd642f2cc09768ff7efe91ba75d4c5fe3922756c971a63daf764011b2","schema_version":"1.0","event_id":"sha256:e442559fd642f2cc09768ff7efe91ba75d4c5fe3922756c971a63daf764011b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:DPU5ET5HIWDONDGY5X25UHBMMA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the typical rank of real bivariate polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Edoardo Ballico","submitted_at":"2012-04-14T10:36:28Z","abstract_excerpt":"Here we study the typical rank for real bivariate homogeneous polynomials of degree $d\\ge 6$ (the case $d\\le 5$ being settled by P. Comon and G. Ottaviani). We prove that $d-1$ is a typical rank and that if $d$ is odd, then $(d+3)/2$ is a typical rank."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3161","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":"2026-05-18T03:57:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1znvwBfi2CagwO0LP98LUkhl5ZS65G15MavRXq4JZN1IoclOB3dNfnmar9gmuDGjj2vddvmr4n+CAIn0vH9GCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:07:43.009412Z"},"content_sha256":"8b5d3f4d565fad748fecef60b9621ac4af8bc5c02545b0b3bab4a8906dfc0f83","schema_version":"1.0","event_id":"sha256:8b5d3f4d565fad748fecef60b9621ac4af8bc5c02545b0b3bab4a8906dfc0f83"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DPU5ET5HIWDONDGY5X25UHBMMA/bundle.json","state_url":"https://pith.science/pith/DPU5ET5HIWDONDGY5X25UHBMMA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DPU5ET5HIWDONDGY5X25UHBMMA/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":"2026-05-30T11:07:43Z","links":{"resolver":"https://pith.science/pith/DPU5ET5HIWDONDGY5X25UHBMMA","bundle":"https://pith.science/pith/DPU5ET5HIWDONDGY5X25UHBMMA/bundle.json","state":"https://pith.science/pith/DPU5ET5HIWDONDGY5X25UHBMMA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DPU5ET5HIWDONDGY5X25UHBMMA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DPU5ET5HIWDONDGY5X25UHBMMA","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":"171bc5b94ec3ba302290baf60170ff08a03ff5107f52037578a1677b2b3df3d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-14T10:36:28Z","title_canon_sha256":"64570e1b65a2e2e68bd83bfbebd17513643d48743ee78584f13b0e7a4f0ab41e"},"schema_version":"1.0","source":{"id":"1204.3161","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3161","created_at":"2026-05-18T03:57:52Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3161v1","created_at":"2026-05-18T03:57:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3161","created_at":"2026-05-18T03:57:52Z"},{"alias_kind":"pith_short_12","alias_value":"DPU5ET5HIWDO","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DPU5ET5HIWDONDGY","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DPU5ET5H","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:8b5d3f4d565fad748fecef60b9621ac4af8bc5c02545b0b3bab4a8906dfc0f83","target":"graph","created_at":"2026-05-18T03:57:52Z","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":"Here we study the typical rank for real bivariate homogeneous polynomials of degree $d\\ge 6$ (the case $d\\le 5$ being settled by P. Comon and G. Ottaviani). We prove that $d-1$ is a typical rank and that if $d$ is odd, then $(d+3)/2$ is a typical rank.","authors_text":"Edoardo Ballico","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-14T10:36:28Z","title":"On the typical rank of real bivariate polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3161","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:e442559fd642f2cc09768ff7efe91ba75d4c5fe3922756c971a63daf764011b2","target":"record","created_at":"2026-05-18T03:57:52Z","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":"171bc5b94ec3ba302290baf60170ff08a03ff5107f52037578a1677b2b3df3d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-14T10:36:28Z","title_canon_sha256":"64570e1b65a2e2e68bd83bfbebd17513643d48743ee78584f13b0e7a4f0ab41e"},"schema_version":"1.0","source":{"id":"1204.3161","kind":"arxiv","version":1}},"canonical_sha256":"1be9d24fa74586e68cd8edf5da1c2c602cdc7f81c7a10d9186dcebbdd69ffdaa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1be9d24fa74586e68cd8edf5da1c2c602cdc7f81c7a10d9186dcebbdd69ffdaa","first_computed_at":"2026-05-18T03:57:52.420698Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:52.420698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R9gUqCkfyFq6qD/3RFkjvcGe2zuUIOeUQBf5FwGBTziyWoywOljbcmQY20ZEuwjz2qR6SWLh4MYCKIC/xL8aBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:52.421455Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.3161","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e442559fd642f2cc09768ff7efe91ba75d4c5fe3922756c971a63daf764011b2","sha256:8b5d3f4d565fad748fecef60b9621ac4af8bc5c02545b0b3bab4a8906dfc0f83"],"state_sha256":"409c9213a285d8c5e99e51e39b5b7275e935f8c243a998c1b4c1614e4d7c3103"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8kIgK1rSfVtDHWVe4De6iLWDTBsqKtTUJoAYC8w+ozLKVaNe87Md33y9+FDnqkwfs5dZujQP/Z1Vhbn09yDzCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T11:07:43.012816Z","bundle_sha256":"e93a3359cadb61400abde4edcca928dac4b033b3dcaa711a59deff2ffb8ee0f8"}}