{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:URIBCAX4ITSAIYLYRMMD7MWLOP","short_pith_number":"pith:URIBCAX4","canonical_record":{"source":{"id":"1810.09373","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-22T15:43:26Z","cross_cats_sorted":[],"title_canon_sha256":"487a518698b0d021c0ef84d4730e613b0fc553b2c223abb18371a65005feb30d","abstract_canon_sha256":"44e65d3bfdbc7a4e3aa5a88a912edc9f06637a23d54b5ea0517cb898934ccfe4"},"schema_version":"1.0"},"canonical_sha256":"a4501102fc44e40461788b183fb2cb73e76342cc6b897d381445a3ba14335a56","source":{"kind":"arxiv","id":"1810.09373","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.09373","created_at":"2026-05-18T00:02:40Z"},{"alias_kind":"arxiv_version","alias_value":"1810.09373v1","created_at":"2026-05-18T00:02:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.09373","created_at":"2026-05-18T00:02:40Z"},{"alias_kind":"pith_short_12","alias_value":"URIBCAX4ITSA","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"URIBCAX4ITSAIYLY","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"URIBCAX4","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:URIBCAX4ITSAIYLYRMMD7MWLOP","target":"record","payload":{"canonical_record":{"source":{"id":"1810.09373","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-22T15:43:26Z","cross_cats_sorted":[],"title_canon_sha256":"487a518698b0d021c0ef84d4730e613b0fc553b2c223abb18371a65005feb30d","abstract_canon_sha256":"44e65d3bfdbc7a4e3aa5a88a912edc9f06637a23d54b5ea0517cb898934ccfe4"},"schema_version":"1.0"},"canonical_sha256":"a4501102fc44e40461788b183fb2cb73e76342cc6b897d381445a3ba14335a56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:40.306297Z","signature_b64":"ytNNqvSmzdfE/qU3esL+cEiwaBkFJoW3MEy2k2VlPF1mWPik5RhZSpduD8AfydwSvbjKgmzLZ/X6KvnhmVGiCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4501102fc44e40461788b183fb2cb73e76342cc6b897d381445a3ba14335a56","last_reissued_at":"2026-05-18T00:02:40.305820Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:40.305820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.09373","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":"2026-05-18T00:02:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iyuYwGeRis5ueE/pMvitIuDg8onMWHOwX632rDYClfDBiXOh7wBq0Loi1O2vDIZgi/etvS6SF45xka6Dhsb8BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:04:13.280680Z"},"content_sha256":"80613c74315b933b4e7f4b274a45ae2135fd8596eb2c3c25416c33ae24f14e8f","schema_version":"1.0","event_id":"sha256:80613c74315b933b4e7f4b274a45ae2135fd8596eb2c3c25416c33ae24f14e8f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:URIBCAX4ITSAIYLYRMMD7MWLOP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetric multilinear forms on Hilbert spaces: where do they attain their norm?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Carando, Jorge Tom\\'as Rodr\\'iguez","submitted_at":"2018-10-22T15:43:26Z","abstract_excerpt":"We characterize the sets of norm one vectors $\\mathbf{x}_1,\\ldots,\\mathbf{x}_k$ in a Hilbert space $\\mathcal H$ such that there exists a $k$-linear symmetric form attaining its norm at $(\\textbf{x}_1,\\ldots,\\mathbf{x}_k)$. We prove that in the bilinear case, any two vectors satisfy this property. However, for $k\\ge 3$ only collinear vectors satisfy this property in the complex case, while in the real case this is equivalent to $\\mathbf{x}_1,\\ldots,\\mathbf{x}_k$ spanning a subspace of dimension at most 2. We use these results to obtain some applications to symmetric multilinear forms, symmetric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09373","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":"2026-05-18T00:02:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Moen82ZtraCwGkhouB2hz5T1eBl2oDzKXjtGcGAXLmREkxtFRwdeTkQ722EoYYqUL9FGwq3Rhb5Si218gr30BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:04:13.281012Z"},"content_sha256":"8ce834243743614f7bacde11966139732c65e91e44a31b9bf7d0bc7023c3d6a9","schema_version":"1.0","event_id":"sha256:8ce834243743614f7bacde11966139732c65e91e44a31b9bf7d0bc7023c3d6a9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/URIBCAX4ITSAIYLYRMMD7MWLOP/bundle.json","state_url":"https://pith.science/pith/URIBCAX4ITSAIYLYRMMD7MWLOP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/URIBCAX4ITSAIYLYRMMD7MWLOP/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":"2026-06-20T06:04:13Z","links":{"resolver":"https://pith.science/pith/URIBCAX4ITSAIYLYRMMD7MWLOP","bundle":"https://pith.science/pith/URIBCAX4ITSAIYLYRMMD7MWLOP/bundle.json","state":"https://pith.science/pith/URIBCAX4ITSAIYLYRMMD7MWLOP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/URIBCAX4ITSAIYLYRMMD7MWLOP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:URIBCAX4ITSAIYLYRMMD7MWLOP","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":"44e65d3bfdbc7a4e3aa5a88a912edc9f06637a23d54b5ea0517cb898934ccfe4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-22T15:43:26Z","title_canon_sha256":"487a518698b0d021c0ef84d4730e613b0fc553b2c223abb18371a65005feb30d"},"schema_version":"1.0","source":{"id":"1810.09373","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.09373","created_at":"2026-05-18T00:02:40Z"},{"alias_kind":"arxiv_version","alias_value":"1810.09373v1","created_at":"2026-05-18T00:02:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.09373","created_at":"2026-05-18T00:02:40Z"},{"alias_kind":"pith_short_12","alias_value":"URIBCAX4ITSA","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"URIBCAX4ITSAIYLY","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"URIBCAX4","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:8ce834243743614f7bacde11966139732c65e91e44a31b9bf7d0bc7023c3d6a9","target":"graph","created_at":"2026-05-18T00:02:40Z","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":"We characterize the sets of norm one vectors $\\mathbf{x}_1,\\ldots,\\mathbf{x}_k$ in a Hilbert space $\\mathcal H$ such that there exists a $k$-linear symmetric form attaining its norm at $(\\textbf{x}_1,\\ldots,\\mathbf{x}_k)$. We prove that in the bilinear case, any two vectors satisfy this property. However, for $k\\ge 3$ only collinear vectors satisfy this property in the complex case, while in the real case this is equivalent to $\\mathbf{x}_1,\\ldots,\\mathbf{x}_k$ spanning a subspace of dimension at most 2. We use these results to obtain some applications to symmetric multilinear forms, symmetric","authors_text":"Daniel Carando, Jorge Tom\\'as Rodr\\'iguez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-22T15:43:26Z","title":"Symmetric multilinear forms on Hilbert spaces: where do they attain their norm?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09373","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":"sha256:80613c74315b933b4e7f4b274a45ae2135fd8596eb2c3c25416c33ae24f14e8f","target":"record","created_at":"2026-05-18T00:02:40Z","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":"44e65d3bfdbc7a4e3aa5a88a912edc9f06637a23d54b5ea0517cb898934ccfe4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-22T15:43:26Z","title_canon_sha256":"487a518698b0d021c0ef84d4730e613b0fc553b2c223abb18371a65005feb30d"},"schema_version":"1.0","source":{"id":"1810.09373","kind":"arxiv","version":1}},"canonical_sha256":"a4501102fc44e40461788b183fb2cb73e76342cc6b897d381445a3ba14335a56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4501102fc44e40461788b183fb2cb73e76342cc6b897d381445a3ba14335a56","first_computed_at":"2026-05-18T00:02:40.305820Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:40.305820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ytNNqvSmzdfE/qU3esL+cEiwaBkFJoW3MEy2k2VlPF1mWPik5RhZSpduD8AfydwSvbjKgmzLZ/X6KvnhmVGiCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:40.306297Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.09373","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80613c74315b933b4e7f4b274a45ae2135fd8596eb2c3c25416c33ae24f14e8f","sha256:8ce834243743614f7bacde11966139732c65e91e44a31b9bf7d0bc7023c3d6a9"],"state_sha256":"62368db5066c8e9dce52aa4b1365e727715c77f91e4185ab34a236bc7039656f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JNoyXamXdwUTwVQGAEoC6jEjVvmw1VBsOk5gLD+IoF8bM9N6xqDgklnp9WCgdmAZIIqiRJeZDo+5vUDc3n6bCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:04:13.282891Z","bundle_sha256":"21d0328e97c36c6ed7baa4fc36a6cc1e145b03ef7b09441b9181598445d4c53c"}}