{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ZJPQSLSMA6ABZVNPN2MX64F5MZ","short_pith_number":"pith:ZJPQSLSM","canonical_record":{"source":{"id":"1406.5892","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-06-23T13:17:13Z","cross_cats_sorted":[],"title_canon_sha256":"907ef7535aaea34f57d11623892c182180394c0acba1ae10df1eb162c56142a4","abstract_canon_sha256":"c1e354a2b0ce6fd61d0ef7859fdb7c2eb3404e441c0a66afecacb1fcb81cee16"},"schema_version":"1.0"},"canonical_sha256":"ca5f092e4c07801cd5af6e997f70bd666d1db1712bde7670e300ca755093dc4e","source":{"kind":"arxiv","id":"1406.5892","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5892","created_at":"2026-05-18T01:12:18Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5892v2","created_at":"2026-05-18T01:12:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5892","created_at":"2026-05-18T01:12:18Z"},{"alias_kind":"pith_short_12","alias_value":"ZJPQSLSMA6AB","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZJPQSLSMA6ABZVNP","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZJPQSLSM","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ZJPQSLSMA6ABZVNPN2MX64F5MZ","target":"record","payload":{"canonical_record":{"source":{"id":"1406.5892","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-06-23T13:17:13Z","cross_cats_sorted":[],"title_canon_sha256":"907ef7535aaea34f57d11623892c182180394c0acba1ae10df1eb162c56142a4","abstract_canon_sha256":"c1e354a2b0ce6fd61d0ef7859fdb7c2eb3404e441c0a66afecacb1fcb81cee16"},"schema_version":"1.0"},"canonical_sha256":"ca5f092e4c07801cd5af6e997f70bd666d1db1712bde7670e300ca755093dc4e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:18.763614Z","signature_b64":"dVHErhvOoR7umQzmv+WjXPKvP4m6POTzv/Hmw3h+5f3Kvpojx8qu/C00EqTWqoOAL4OqoLgK0wCQpIzH3Y4XDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca5f092e4c07801cd5af6e997f70bd666d1db1712bde7670e300ca755093dc4e","last_reissued_at":"2026-05-18T01:12:18.763261Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:18.763261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.5892","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":"2026-05-18T01:12:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rEgbvjiVxmV88syWoCzSLHWL7EgAnEl0DerOfz056m25YuNMc/OfykCznLpVhQpDRiWGQrvsnGMgF4wILmMKDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:56:48.561856Z"},"content_sha256":"5f72a22fdfb38f88fb545eb9a5d6679a0e6946ab565fc8af4f4b06ad213b2aa9","schema_version":"1.0","event_id":"sha256:5f72a22fdfb38f88fb545eb9a5d6679a0e6946ab565fc8af4f4b06ad213b2aa9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ZJPQSLSMA6ABZVNPN2MX64F5MZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability index for algebras with involution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Thomas Unger, Vincent Astier","submitted_at":"2014-06-23T13:17:13Z","abstract_excerpt":"In earlier work we developed the theory of signatures of hermitian forms over algebras with involution with respect to orderings on the base field of the algebra and obtained in particular that the total signature of a hermitian form is a continuous function from the space of orderings of that field to $\\mathbb{Z}$. In this note we give another presentation of signatures and also introduce and study the stability index of algebras with involution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5892","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":"2026-05-18T01:12:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yjtI7j5FbmITo2LChXDR8Rm34YcmL+nYodzQxECl/8EIYryHgGbx+qH8V26hItmmsASvKCs6qiP1jFBw8cVPBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:56:48.562202Z"},"content_sha256":"9693d7d706bb3db7685bd70e880ca98f637228b6499fa6089e2afcc97c6b5715","schema_version":"1.0","event_id":"sha256:9693d7d706bb3db7685bd70e880ca98f637228b6499fa6089e2afcc97c6b5715"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZJPQSLSMA6ABZVNPN2MX64F5MZ/bundle.json","state_url":"https://pith.science/pith/ZJPQSLSMA6ABZVNPN2MX64F5MZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZJPQSLSMA6ABZVNPN2MX64F5MZ/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":"2026-06-02T22:56:48Z","links":{"resolver":"https://pith.science/pith/ZJPQSLSMA6ABZVNPN2MX64F5MZ","bundle":"https://pith.science/pith/ZJPQSLSMA6ABZVNPN2MX64F5MZ/bundle.json","state":"https://pith.science/pith/ZJPQSLSMA6ABZVNPN2MX64F5MZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZJPQSLSMA6ABZVNPN2MX64F5MZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZJPQSLSMA6ABZVNPN2MX64F5MZ","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":"c1e354a2b0ce6fd61d0ef7859fdb7c2eb3404e441c0a66afecacb1fcb81cee16","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-06-23T13:17:13Z","title_canon_sha256":"907ef7535aaea34f57d11623892c182180394c0acba1ae10df1eb162c56142a4"},"schema_version":"1.0","source":{"id":"1406.5892","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5892","created_at":"2026-05-18T01:12:18Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5892v2","created_at":"2026-05-18T01:12:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5892","created_at":"2026-05-18T01:12:18Z"},{"alias_kind":"pith_short_12","alias_value":"ZJPQSLSMA6AB","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZJPQSLSMA6ABZVNP","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZJPQSLSM","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:9693d7d706bb3db7685bd70e880ca98f637228b6499fa6089e2afcc97c6b5715","target":"graph","created_at":"2026-05-18T01:12:18Z","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":"In earlier work we developed the theory of signatures of hermitian forms over algebras with involution with respect to orderings on the base field of the algebra and obtained in particular that the total signature of a hermitian form is a continuous function from the space of orderings of that field to $\\mathbb{Z}$. In this note we give another presentation of signatures and also introduce and study the stability index of algebras with involution.","authors_text":"Thomas Unger, Vincent Astier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-06-23T13:17:13Z","title":"Stability index for algebras with involution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5892","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":"sha256:5f72a22fdfb38f88fb545eb9a5d6679a0e6946ab565fc8af4f4b06ad213b2aa9","target":"record","created_at":"2026-05-18T01:12:18Z","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":"c1e354a2b0ce6fd61d0ef7859fdb7c2eb3404e441c0a66afecacb1fcb81cee16","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-06-23T13:17:13Z","title_canon_sha256":"907ef7535aaea34f57d11623892c182180394c0acba1ae10df1eb162c56142a4"},"schema_version":"1.0","source":{"id":"1406.5892","kind":"arxiv","version":2}},"canonical_sha256":"ca5f092e4c07801cd5af6e997f70bd666d1db1712bde7670e300ca755093dc4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca5f092e4c07801cd5af6e997f70bd666d1db1712bde7670e300ca755093dc4e","first_computed_at":"2026-05-18T01:12:18.763261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:18.763261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dVHErhvOoR7umQzmv+WjXPKvP4m6POTzv/Hmw3h+5f3Kvpojx8qu/C00EqTWqoOAL4OqoLgK0wCQpIzH3Y4XDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:18.763614Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.5892","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f72a22fdfb38f88fb545eb9a5d6679a0e6946ab565fc8af4f4b06ad213b2aa9","sha256:9693d7d706bb3db7685bd70e880ca98f637228b6499fa6089e2afcc97c6b5715"],"state_sha256":"db76f8cd85c24991dc99f59588044d8c3be7ad5f6fe29055a112517f17731149"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K6k76XGdgXMfIhXNnRV36rU8AC5DN6btyXe5y1q+PmW13pG6yH5wQfWrBAmy1ZfNS/Wq4TmL28S2nzKQcGfJCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T22:56:48.564112Z","bundle_sha256":"66e051fbd513722d73e7c6ac988090bd9ce13d4c7507182f470c5163a8ba282c"}}