{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:KT2UABBAQL6FKR2TAL3VZ2QP2K","short_pith_number":"pith:KT2UABBA","canonical_record":{"source":{"id":"0707.3754","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2007-07-25T14:26:54Z","cross_cats_sorted":[],"title_canon_sha256":"35bd19ccacad723f511c1978ddb1fcb793935583c50da6d39f2c0fe7f20f949a","abstract_canon_sha256":"f303f46b2c7473b26a7abb76486b4c7d5112455102b9a0de10c72a3d476febe3"},"schema_version":"1.0"},"canonical_sha256":"54f540042082fc55475302f75cea0fd2ba156940769d6258a9aef67ab92038e8","source":{"kind":"arxiv","id":"0707.3754","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.3754","created_at":"2026-05-18T04:03:07Z"},{"alias_kind":"arxiv_version","alias_value":"0707.3754v3","created_at":"2026-05-18T04:03:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.3754","created_at":"2026-05-18T04:03:07Z"},{"alias_kind":"pith_short_12","alias_value":"KT2UABBAQL6F","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"KT2UABBAQL6FKR2T","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"KT2UABBA","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:KT2UABBAQL6FKR2TAL3VZ2QP2K","target":"record","payload":{"canonical_record":{"source":{"id":"0707.3754","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2007-07-25T14:26:54Z","cross_cats_sorted":[],"title_canon_sha256":"35bd19ccacad723f511c1978ddb1fcb793935583c50da6d39f2c0fe7f20f949a","abstract_canon_sha256":"f303f46b2c7473b26a7abb76486b4c7d5112455102b9a0de10c72a3d476febe3"},"schema_version":"1.0"},"canonical_sha256":"54f540042082fc55475302f75cea0fd2ba156940769d6258a9aef67ab92038e8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:07.765669Z","signature_b64":"Lz/G+jH0vxkWbFw2Zwx6fvih5K+v+VERl5yefrvJWqwIbLH/0LYSRrgD0JrC2H0XU6wcD3Hx7EuZSBWvfKiuAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54f540042082fc55475302f75cea0fd2ba156940769d6258a9aef67ab92038e8","last_reissued_at":"2026-05-18T04:03:07.764849Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:07.764849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0707.3754","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:03:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t7FlYx9vrMA1gLyh1pRDVHiVIO2z2Ci3+PhNwsCEZShcWfCdEYKLAJS93t0afDjTapIfD0D3wVMq3CramOgkDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:22:25.389736Z"},"content_sha256":"555feacf31254ac0eb5a15d74bb6712c4ea1550495c08067d2e3028cfe3a5ae1","schema_version":"1.0","event_id":"sha256:555feacf31254ac0eb5a15d74bb6712c4ea1550495c08067d2e3028cfe3a5ae1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:KT2UABBAQL6FKR2TAL3VZ2QP2K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A hermitian analogue of the Broecker-Prestel theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Thomas Unger, Vincent Astier","submitted_at":"2007-07-25T14:26:54Z","abstract_excerpt":"The Broecker-Prestel local-global principle characterizes weak isotropy of quadratic forms over a formally real field in terms of weak isotropy over the henselizations and isotropy over the real closures of that field. A hermitian analogue of this principle is presented for algebras of index at most two. An improved result is also presented for algebras with a decomposable involution, algebras of pythagorean index at most two, and algebras over SAP and ED fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.3754","kind":"arxiv","version":3},"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":"2026-05-18T04:03:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qhmruaV3WSR06iRfndAlGb3tByPLLnHMe/qeKukkDpNVKHt5XcmTW83D5eBLiAhDHaIaSf4//iwMeWznbsuwCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:22:25.390075Z"},"content_sha256":"1396a8f7f83328deab442ed10a003655e209ff344101285a0d11f7c1a1f5bd44","schema_version":"1.0","event_id":"sha256:1396a8f7f83328deab442ed10a003655e209ff344101285a0d11f7c1a1f5bd44"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KT2UABBAQL6FKR2TAL3VZ2QP2K/bundle.json","state_url":"https://pith.science/pith/KT2UABBAQL6FKR2TAL3VZ2QP2K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KT2UABBAQL6FKR2TAL3VZ2QP2K/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":"2026-06-03T07:22:25Z","links":{"resolver":"https://pith.science/pith/KT2UABBAQL6FKR2TAL3VZ2QP2K","bundle":"https://pith.science/pith/KT2UABBAQL6FKR2TAL3VZ2QP2K/bundle.json","state":"https://pith.science/pith/KT2UABBAQL6FKR2TAL3VZ2QP2K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KT2UABBAQL6FKR2TAL3VZ2QP2K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:KT2UABBAQL6FKR2TAL3VZ2QP2K","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":"f303f46b2c7473b26a7abb76486b4c7d5112455102b9a0de10c72a3d476febe3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2007-07-25T14:26:54Z","title_canon_sha256":"35bd19ccacad723f511c1978ddb1fcb793935583c50da6d39f2c0fe7f20f949a"},"schema_version":"1.0","source":{"id":"0707.3754","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.3754","created_at":"2026-05-18T04:03:07Z"},{"alias_kind":"arxiv_version","alias_value":"0707.3754v3","created_at":"2026-05-18T04:03:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.3754","created_at":"2026-05-18T04:03:07Z"},{"alias_kind":"pith_short_12","alias_value":"KT2UABBAQL6F","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"KT2UABBAQL6FKR2T","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"KT2UABBA","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:1396a8f7f83328deab442ed10a003655e209ff344101285a0d11f7c1a1f5bd44","target":"graph","created_at":"2026-05-18T04:03:07Z","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":"The Broecker-Prestel local-global principle characterizes weak isotropy of quadratic forms over a formally real field in terms of weak isotropy over the henselizations and isotropy over the real closures of that field. A hermitian analogue of this principle is presented for algebras of index at most two. An improved result is also presented for algebras with a decomposable involution, algebras of pythagorean index at most two, and algebras over SAP and ED fields.","authors_text":"Thomas Unger, Vincent Astier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2007-07-25T14:26:54Z","title":"A hermitian analogue of the Broecker-Prestel theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.3754","kind":"arxiv","version":3},"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":"sha256:555feacf31254ac0eb5a15d74bb6712c4ea1550495c08067d2e3028cfe3a5ae1","target":"record","created_at":"2026-05-18T04:03:07Z","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":"f303f46b2c7473b26a7abb76486b4c7d5112455102b9a0de10c72a3d476febe3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2007-07-25T14:26:54Z","title_canon_sha256":"35bd19ccacad723f511c1978ddb1fcb793935583c50da6d39f2c0fe7f20f949a"},"schema_version":"1.0","source":{"id":"0707.3754","kind":"arxiv","version":3}},"canonical_sha256":"54f540042082fc55475302f75cea0fd2ba156940769d6258a9aef67ab92038e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54f540042082fc55475302f75cea0fd2ba156940769d6258a9aef67ab92038e8","first_computed_at":"2026-05-18T04:03:07.764849Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:07.764849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lz/G+jH0vxkWbFw2Zwx6fvih5K+v+VERl5yefrvJWqwIbLH/0LYSRrgD0JrC2H0XU6wcD3Hx7EuZSBWvfKiuAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:07.765669Z","signed_message":"canonical_sha256_bytes"},"source_id":"0707.3754","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:555feacf31254ac0eb5a15d74bb6712c4ea1550495c08067d2e3028cfe3a5ae1","sha256:1396a8f7f83328deab442ed10a003655e209ff344101285a0d11f7c1a1f5bd44"],"state_sha256":"cf215979e36a644144dbb74deaaa3332f5e15ea51e3ad5c2239cc34d09f152a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m98t/0cTjdtQTAUpHQUVa7sK2fvsBA58T4ryfFBTb8WWAxBo97QILNBOBS8B35o9cLPjShO9NsTe4/PW1jKvAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T07:22:25.392822Z","bundle_sha256":"e694bec86967a8d2020ed4224600f7fdf315d06b892545398516ab4fd8bbee36"}}