{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BO6QHP3YA7S5AF4BHAUTUMDYLA","short_pith_number":"pith:BO6QHP3Y","canonical_record":{"source":{"id":"1312.3494","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-12T14:35:13Z","cross_cats_sorted":[],"title_canon_sha256":"b7b7116ed18cc077d486d0c455ca0b769ef8e8ddaf0fe3a8cc8dd96ec348beb4","abstract_canon_sha256":"2c373f0dc2827e1f80b9d3bc5af14198626cce7e9ac432fdb4bf7ab4a7c1538c"},"schema_version":"1.0"},"canonical_sha256":"0bbd03bf7807e5d0178138293a307858146c0c15d1e5f59fcb042d3b713faa38","source":{"kind":"arxiv","id":"1312.3494","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3494","created_at":"2026-05-18T00:19:04Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3494v2","created_at":"2026-05-18T00:19:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3494","created_at":"2026-05-18T00:19:04Z"},{"alias_kind":"pith_short_12","alias_value":"BO6QHP3YA7S5","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BO6QHP3YA7S5AF4B","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BO6QHP3Y","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BO6QHP3YA7S5AF4BHAUTUMDYLA","target":"record","payload":{"canonical_record":{"source":{"id":"1312.3494","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-12T14:35:13Z","cross_cats_sorted":[],"title_canon_sha256":"b7b7116ed18cc077d486d0c455ca0b769ef8e8ddaf0fe3a8cc8dd96ec348beb4","abstract_canon_sha256":"2c373f0dc2827e1f80b9d3bc5af14198626cce7e9ac432fdb4bf7ab4a7c1538c"},"schema_version":"1.0"},"canonical_sha256":"0bbd03bf7807e5d0178138293a307858146c0c15d1e5f59fcb042d3b713faa38","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:04.862410Z","signature_b64":"rrK5x8zZgCVzt7gH0wnJ7zagzehM9FlZ/XafoYONv4UwbSgvECkmkJA6rbYEabma4mn3SQYbTtFem6dPJKuACA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bbd03bf7807e5d0178138293a307858146c0c15d1e5f59fcb042d3b713faa38","last_reissued_at":"2026-05-18T00:19:04.861838Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:04.861838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.3494","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":"2026-05-18T00:19:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aG/JtQ1MDpZS+j/4mrYvCQ+Hcom908WwBUqkfW9YhK/qxS+KPesCfmTSHuuE2g6QIJ3O6zICIg721g5XbN/HCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T23:16:09.128887Z"},"content_sha256":"f6b1eb7900882f6562c024410be87f7e2803eaf1b07cf20def567a36ddc38325","schema_version":"1.0","event_id":"sha256:f6b1eb7900882f6562c024410be87f7e2803eaf1b07cf20def567a36ddc38325"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BO6QHP3YA7S5AF4BHAUTUMDYLA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generic Power Sum Decompositions and Bounds for the Waring Rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alessandro De Paris, Edoardo Ballico","submitted_at":"2013-12-12T14:35:13Z","abstract_excerpt":"A notion of open rank, related with generic power sum decompositions of forms, has recently been introduced in the literature. The main result here is that the maximum open rank for plane quartics is eight. In particular, this gives the first example of $n,d$, such that the maximum open rank for degree $d$ forms that essentially depend on $n$ variables is strictly greater than the maximum rank. On one hand, the result allows to improve the previously known bounds on open rank, but on the other hand indicates that such bounds are likely quite relaxed. Nevertheless, some of the preparatory resul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3494","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":""},"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":"2026-05-18T00:19:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4IMwJhFpub1zdHRXa8T1DxFNwLYKVnb98S71g6rYnwIinfQF6CggH6Zi7fVJe5DRUZQ8zB6Kef41qimd9WohBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T23:16:09.129219Z"},"content_sha256":"af56552af1e65fba0443c0fc2dfd909b72bda9c204708e529de127628b97db8d","schema_version":"1.0","event_id":"sha256:af56552af1e65fba0443c0fc2dfd909b72bda9c204708e529de127628b97db8d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BO6QHP3YA7S5AF4BHAUTUMDYLA/bundle.json","state_url":"https://pith.science/pith/BO6QHP3YA7S5AF4BHAUTUMDYLA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BO6QHP3YA7S5AF4BHAUTUMDYLA/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":"2026-06-20T23:16:09Z","links":{"resolver":"https://pith.science/pith/BO6QHP3YA7S5AF4BHAUTUMDYLA","bundle":"https://pith.science/pith/BO6QHP3YA7S5AF4BHAUTUMDYLA/bundle.json","state":"https://pith.science/pith/BO6QHP3YA7S5AF4BHAUTUMDYLA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BO6QHP3YA7S5AF4BHAUTUMDYLA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BO6QHP3YA7S5AF4BHAUTUMDYLA","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":"2c373f0dc2827e1f80b9d3bc5af14198626cce7e9ac432fdb4bf7ab4a7c1538c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-12T14:35:13Z","title_canon_sha256":"b7b7116ed18cc077d486d0c455ca0b769ef8e8ddaf0fe3a8cc8dd96ec348beb4"},"schema_version":"1.0","source":{"id":"1312.3494","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3494","created_at":"2026-05-18T00:19:04Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3494v2","created_at":"2026-05-18T00:19:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3494","created_at":"2026-05-18T00:19:04Z"},{"alias_kind":"pith_short_12","alias_value":"BO6QHP3YA7S5","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BO6QHP3YA7S5AF4B","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BO6QHP3Y","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:af56552af1e65fba0443c0fc2dfd909b72bda9c204708e529de127628b97db8d","target":"graph","created_at":"2026-05-18T00:19:04Z","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":"A notion of open rank, related with generic power sum decompositions of forms, has recently been introduced in the literature. The main result here is that the maximum open rank for plane quartics is eight. In particular, this gives the first example of $n,d$, such that the maximum open rank for degree $d$ forms that essentially depend on $n$ variables is strictly greater than the maximum rank. On one hand, the result allows to improve the previously known bounds on open rank, but on the other hand indicates that such bounds are likely quite relaxed. Nevertheless, some of the preparatory resul","authors_text":"Alessandro De Paris, Edoardo Ballico","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-12T14:35:13Z","title":"Generic Power Sum Decompositions and Bounds for the Waring Rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3494","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:f6b1eb7900882f6562c024410be87f7e2803eaf1b07cf20def567a36ddc38325","target":"record","created_at":"2026-05-18T00:19:04Z","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":"2c373f0dc2827e1f80b9d3bc5af14198626cce7e9ac432fdb4bf7ab4a7c1538c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-12T14:35:13Z","title_canon_sha256":"b7b7116ed18cc077d486d0c455ca0b769ef8e8ddaf0fe3a8cc8dd96ec348beb4"},"schema_version":"1.0","source":{"id":"1312.3494","kind":"arxiv","version":2}},"canonical_sha256":"0bbd03bf7807e5d0178138293a307858146c0c15d1e5f59fcb042d3b713faa38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0bbd03bf7807e5d0178138293a307858146c0c15d1e5f59fcb042d3b713faa38","first_computed_at":"2026-05-18T00:19:04.861838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:04.861838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rrK5x8zZgCVzt7gH0wnJ7zagzehM9FlZ/XafoYONv4UwbSgvECkmkJA6rbYEabma4mn3SQYbTtFem6dPJKuACA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:04.862410Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.3494","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6b1eb7900882f6562c024410be87f7e2803eaf1b07cf20def567a36ddc38325","sha256:af56552af1e65fba0443c0fc2dfd909b72bda9c204708e529de127628b97db8d"],"state_sha256":"275d420f991ae2fb5c9661ac371084500bf65c81c5ce5e9af6bb46ca295f1c56"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LQyvoyly/In+2kLFYKpFYbIrNTea858roGTgSs/qDKQG7D91u4Y9nmbUtPvZm+Ows2mw3Nbe5PbcTaySDvrDCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T23:16:09.131068Z","bundle_sha256":"74c282752624e799c57f81c17af64b4761a069db1bbf6dad343ff272fcc59bce"}}