{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:2SUEJGL5SSNUVYMLF4PMA64JYI","short_pith_number":"pith:2SUEJGL5","canonical_record":{"source":{"id":"1006.5127","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-06-26T10:20:49Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"08543f6365cefca739cd0f5b3a619446102fcaa874ea21329d49a807a10846fe","abstract_canon_sha256":"859d3357862b750e40d0c257bc916b27ece707be4350820318806390e318a3d3"},"schema_version":"1.0"},"canonical_sha256":"d4a844997d949b4ae18b2f1ec07b89c20ad9a78f864cdad008dbeb5f8943e54f","source":{"kind":"arxiv","id":"1006.5127","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.5127","created_at":"2026-06-03T23:06:38Z"},{"alias_kind":"arxiv_version","alias_value":"1006.5127v1","created_at":"2026-06-03T23:06:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5127","created_at":"2026-06-03T23:06:38Z"},{"alias_kind":"pith_short_12","alias_value":"2SUEJGL5SSNU","created_at":"2026-06-03T23:06:38Z"},{"alias_kind":"pith_short_16","alias_value":"2SUEJGL5SSNUVYML","created_at":"2026-06-03T23:06:38Z"},{"alias_kind":"pith_short_8","alias_value":"2SUEJGL5","created_at":"2026-06-03T23:06:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:2SUEJGL5SSNUVYMLF4PMA64JYI","target":"record","payload":{"canonical_record":{"source":{"id":"1006.5127","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-06-26T10:20:49Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"08543f6365cefca739cd0f5b3a619446102fcaa874ea21329d49a807a10846fe","abstract_canon_sha256":"859d3357862b750e40d0c257bc916b27ece707be4350820318806390e318a3d3"},"schema_version":"1.0"},"canonical_sha256":"d4a844997d949b4ae18b2f1ec07b89c20ad9a78f864cdad008dbeb5f8943e54f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T23:06:38.974057Z","signature_b64":"jzm4VuynVICmAgB47EflfYcZXSNpkmNqeAvdyWlmBMl8MKZDZ3cRjyLlwspM7sD/b4zAKQ9o6fNhDVg+Bf+CAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4a844997d949b4ae18b2f1ec07b89c20ad9a78f864cdad008dbeb5f8943e54f","last_reissued_at":"2026-06-03T23:06:38.973659Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T23:06:38.973659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.5127","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":"2026-06-03T23:06:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cMGcX6eQsPN1dpB412+SGvPhtp90A9ZiVS3mDSP0qJ/hDEdwP1XTe0c1zag//pLeOSFLEF1toHT2ctMDb3VtAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T14:21:24.408028Z"},"content_sha256":"a73e58972f7b40006139567804564958be89c70dd4274a8b9f691cf2715ab5d0","schema_version":"1.0","event_id":"sha256:a73e58972f7b40006139567804564958be89c70dd4274a8b9f691cf2715ab5d0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:2SUEJGL5SSNUVYMLF4PMA64JYI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the maximum rank of a real binary form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.AG","authors_text":"Antonio Causa, Riccardo Re","submitted_at":"2010-06-26T10:20:49Z","abstract_excerpt":"We show that a real homogeneous polynomial f(x,y) with distinct roots and degree d greater or equal than 3 has d real roots if and only if for any (a,b) not equal to (0,0) the polynomial af_x+bf_y has d-1 real roots. This answers to a question posed by P. Comon and G. Ottaviani, and shows that the interior part of the locus of degree d binary real binary forms of rank equal to d is given exactly by the forms with d real roots."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5127","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1006.5127/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":"2026-06-03T23:06:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mqmh8EC1dQQHrfNUMS3zcV4LUFKZpRl/ZdM/ylOdVujdW82XtR3/+PdeRNyw2XqYmrUXnG7nbNBzGA6ai4GuCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T14:21:24.408416Z"},"content_sha256":"d92594fb1738a1ff1bf07ba9ffe95bfe6d5f26540854696c087c2c8c7b3fcc38","schema_version":"1.0","event_id":"sha256:d92594fb1738a1ff1bf07ba9ffe95bfe6d5f26540854696c087c2c8c7b3fcc38"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2SUEJGL5SSNUVYMLF4PMA64JYI/bundle.json","state_url":"https://pith.science/pith/2SUEJGL5SSNUVYMLF4PMA64JYI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2SUEJGL5SSNUVYMLF4PMA64JYI/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":"2026-06-21T14:21:24Z","links":{"resolver":"https://pith.science/pith/2SUEJGL5SSNUVYMLF4PMA64JYI","bundle":"https://pith.science/pith/2SUEJGL5SSNUVYMLF4PMA64JYI/bundle.json","state":"https://pith.science/pith/2SUEJGL5SSNUVYMLF4PMA64JYI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2SUEJGL5SSNUVYMLF4PMA64JYI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2SUEJGL5SSNUVYMLF4PMA64JYI","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":"859d3357862b750e40d0c257bc916b27ece707be4350820318806390e318a3d3","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-06-26T10:20:49Z","title_canon_sha256":"08543f6365cefca739cd0f5b3a619446102fcaa874ea21329d49a807a10846fe"},"schema_version":"1.0","source":{"id":"1006.5127","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.5127","created_at":"2026-06-03T23:06:38Z"},{"alias_kind":"arxiv_version","alias_value":"1006.5127v1","created_at":"2026-06-03T23:06:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.5127","created_at":"2026-06-03T23:06:38Z"},{"alias_kind":"pith_short_12","alias_value":"2SUEJGL5SSNU","created_at":"2026-06-03T23:06:38Z"},{"alias_kind":"pith_short_16","alias_value":"2SUEJGL5SSNUVYML","created_at":"2026-06-03T23:06:38Z"},{"alias_kind":"pith_short_8","alias_value":"2SUEJGL5","created_at":"2026-06-03T23:06:38Z"}],"graph_snapshots":[{"event_id":"sha256:d92594fb1738a1ff1bf07ba9ffe95bfe6d5f26540854696c087c2c8c7b3fcc38","target":"graph","created_at":"2026-06-03T23:06:38Z","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/1006.5127/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that a real homogeneous polynomial f(x,y) with distinct roots and degree d greater or equal than 3 has d real roots if and only if for any (a,b) not equal to (0,0) the polynomial af_x+bf_y has d-1 real roots. This answers to a question posed by P. Comon and G. Ottaviani, and shows that the interior part of the locus of degree d binary real binary forms of rank equal to d is given exactly by the forms with d real roots.","authors_text":"Antonio Causa, Riccardo Re","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-06-26T10:20:49Z","title":"On the maximum rank of a real binary form"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.5127","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:a73e58972f7b40006139567804564958be89c70dd4274a8b9f691cf2715ab5d0","target":"record","created_at":"2026-06-03T23:06:38Z","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":"859d3357862b750e40d0c257bc916b27ece707be4350820318806390e318a3d3","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-06-26T10:20:49Z","title_canon_sha256":"08543f6365cefca739cd0f5b3a619446102fcaa874ea21329d49a807a10846fe"},"schema_version":"1.0","source":{"id":"1006.5127","kind":"arxiv","version":1}},"canonical_sha256":"d4a844997d949b4ae18b2f1ec07b89c20ad9a78f864cdad008dbeb5f8943e54f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4a844997d949b4ae18b2f1ec07b89c20ad9a78f864cdad008dbeb5f8943e54f","first_computed_at":"2026-06-03T23:06:38.973659Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T23:06:38.973659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jzm4VuynVICmAgB47EflfYcZXSNpkmNqeAvdyWlmBMl8MKZDZ3cRjyLlwspM7sD/b4zAKQ9o6fNhDVg+Bf+CAA==","signature_status":"signed_v1","signed_at":"2026-06-03T23:06:38.974057Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.5127","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a73e58972f7b40006139567804564958be89c70dd4274a8b9f691cf2715ab5d0","sha256:d92594fb1738a1ff1bf07ba9ffe95bfe6d5f26540854696c087c2c8c7b3fcc38"],"state_sha256":"838d170291b22b246a2a90549d3af636b91e0f30cddf8e43134078fff7bc5fc7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dftQel5b+8NlNCflGqm3h13RBMnO153TVkuJtenzh4gePh50ivtzLXmTsg14JHdJSpdsvyIaOV7xIWihK3MGBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T14:21:24.410594Z","bundle_sha256":"3945b6d49eb4b932f1158fa9a03ff586a19be368dcc9cc61610e7e6754692756"}}