{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:DWPZU2WLTJJJRRVG2MYBKNCPSJ","short_pith_number":"pith:DWPZU2WL","canonical_record":{"source":{"id":"1112.1632","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-12-07T17:18:32Z","cross_cats_sorted":[],"title_canon_sha256":"102b6e5cc414e5d881499b8f6232fc766cda8fcf1abd647962ec0afdf521496c","abstract_canon_sha256":"8bcb25cba63e565a4e5cb108c3e863fd3fcb47e4e1fe7bab54ffa7c219d7c6c8"},"schema_version":"1.0"},"canonical_sha256":"1d9f9a6acb9a5298c6a6d33015344f925166ff8d0b6e65cd50b8d5fcd2770f90","source":{"kind":"arxiv","id":"1112.1632","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1632","created_at":"2026-05-18T04:06:46Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1632v1","created_at":"2026-05-18T04:06:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1632","created_at":"2026-05-18T04:06:46Z"},{"alias_kind":"pith_short_12","alias_value":"DWPZU2WLTJJJ","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DWPZU2WLTJJJRRVG","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DWPZU2WL","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:DWPZU2WLTJJJRRVG2MYBKNCPSJ","target":"record","payload":{"canonical_record":{"source":{"id":"1112.1632","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-12-07T17:18:32Z","cross_cats_sorted":[],"title_canon_sha256":"102b6e5cc414e5d881499b8f6232fc766cda8fcf1abd647962ec0afdf521496c","abstract_canon_sha256":"8bcb25cba63e565a4e5cb108c3e863fd3fcb47e4e1fe7bab54ffa7c219d7c6c8"},"schema_version":"1.0"},"canonical_sha256":"1d9f9a6acb9a5298c6a6d33015344f925166ff8d0b6e65cd50b8d5fcd2770f90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:46.625112Z","signature_b64":"v43PJKBoezg9cXuPsj9TP/52owskQFzI5D5EymZ6iTQ+qhrsU6oLgOkvnTLSZUGy2zRanRfqk32BlW93IDlbCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d9f9a6acb9a5298c6a6d33015344f925166ff8d0b6e65cd50b8d5fcd2770f90","last_reissued_at":"2026-05-18T04:06:46.624585Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:46.624585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.1632","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":"2026-05-18T04:06:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K5vFf3BgJ2ghDfcVYWEM456SGeb16FLFDe7cZXivV6A+QdpFQ76n4BZzYnKQhyQsTKdbXB0OkQ5VCoAzH9KFCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T10:45:17.942762Z"},"content_sha256":"3d86858161aa6d01c5769d09ad6c1196ff10c5a0039d19eca72a3688ab240f02","schema_version":"1.0","event_id":"sha256:3d86858161aa6d01c5769d09ad6c1196ff10c5a0039d19eca72a3688ab240f02"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:DWPZU2WLTJJJRRVG2MYBKNCPSJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a family of frames for Krein spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Maestripieri, F. Mart\\'inez Per\\'ia, J. I. Giribet, P. Massey","submitted_at":"2011-12-07T17:18:32Z","abstract_excerpt":"A definition of frames for Krein spaces is proposed, which extends the notion of $J$-orthonormal basis of Krein spaces. A $J$-frame for a Krein space $(\\HH, \\K{\\,}{\\,})$ is in particular a frame for $\\HH$ in the Hilbert space sense. But it is also compatible with the indefinite inner product $\\K{\\,}{\\,}$, meaning that it determines a pair of maximal uniformly $J$-definite subspaces with different positivity, an analogue to the maximal dual pair associated to a $J$-orthonormal basis.\n  Also, each $J$-frame induces an indefinite reconstruction formula for the vectors in $\\HH$, which resembles th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1632","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":"2026-05-18T04:06:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tkd8dCcETvR4GEnOupnPi0lk8xsrWuUshO8FetGIhlzm1ZFgBrhLXKB/GXa+iKyom45bWDFfgLh+V6TRFnmBBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T10:45:17.943521Z"},"content_sha256":"f0c28412c0de8f0f35c9568c51a7236ec80c4d6aa1da91d843d627286faec4dd","schema_version":"1.0","event_id":"sha256:f0c28412c0de8f0f35c9568c51a7236ec80c4d6aa1da91d843d627286faec4dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DWPZU2WLTJJJRRVG2MYBKNCPSJ/bundle.json","state_url":"https://pith.science/pith/DWPZU2WLTJJJRRVG2MYBKNCPSJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DWPZU2WLTJJJRRVG2MYBKNCPSJ/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":"2026-05-23T10:45:17Z","links":{"resolver":"https://pith.science/pith/DWPZU2WLTJJJRRVG2MYBKNCPSJ","bundle":"https://pith.science/pith/DWPZU2WLTJJJRRVG2MYBKNCPSJ/bundle.json","state":"https://pith.science/pith/DWPZU2WLTJJJRRVG2MYBKNCPSJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DWPZU2WLTJJJRRVG2MYBKNCPSJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DWPZU2WLTJJJRRVG2MYBKNCPSJ","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":"8bcb25cba63e565a4e5cb108c3e863fd3fcb47e4e1fe7bab54ffa7c219d7c6c8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-12-07T17:18:32Z","title_canon_sha256":"102b6e5cc414e5d881499b8f6232fc766cda8fcf1abd647962ec0afdf521496c"},"schema_version":"1.0","source":{"id":"1112.1632","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1632","created_at":"2026-05-18T04:06:46Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1632v1","created_at":"2026-05-18T04:06:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1632","created_at":"2026-05-18T04:06:46Z"},{"alias_kind":"pith_short_12","alias_value":"DWPZU2WLTJJJ","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DWPZU2WLTJJJRRVG","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DWPZU2WL","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:f0c28412c0de8f0f35c9568c51a7236ec80c4d6aa1da91d843d627286faec4dd","target":"graph","created_at":"2026-05-18T04:06:46Z","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 definition of frames for Krein spaces is proposed, which extends the notion of $J$-orthonormal basis of Krein spaces. A $J$-frame for a Krein space $(\\HH, \\K{\\,}{\\,})$ is in particular a frame for $\\HH$ in the Hilbert space sense. But it is also compatible with the indefinite inner product $\\K{\\,}{\\,}$, meaning that it determines a pair of maximal uniformly $J$-definite subspaces with different positivity, an analogue to the maximal dual pair associated to a $J$-orthonormal basis.\n  Also, each $J$-frame induces an indefinite reconstruction formula for the vectors in $\\HH$, which resembles th","authors_text":"A. Maestripieri, F. Mart\\'inez Per\\'ia, J. I. Giribet, P. Massey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-12-07T17:18:32Z","title":"On a family of frames for Krein spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1632","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":"sha256:3d86858161aa6d01c5769d09ad6c1196ff10c5a0039d19eca72a3688ab240f02","target":"record","created_at":"2026-05-18T04:06:46Z","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":"8bcb25cba63e565a4e5cb108c3e863fd3fcb47e4e1fe7bab54ffa7c219d7c6c8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-12-07T17:18:32Z","title_canon_sha256":"102b6e5cc414e5d881499b8f6232fc766cda8fcf1abd647962ec0afdf521496c"},"schema_version":"1.0","source":{"id":"1112.1632","kind":"arxiv","version":1}},"canonical_sha256":"1d9f9a6acb9a5298c6a6d33015344f925166ff8d0b6e65cd50b8d5fcd2770f90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d9f9a6acb9a5298c6a6d33015344f925166ff8d0b6e65cd50b8d5fcd2770f90","first_computed_at":"2026-05-18T04:06:46.624585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:46.624585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v43PJKBoezg9cXuPsj9TP/52owskQFzI5D5EymZ6iTQ+qhrsU6oLgOkvnTLSZUGy2zRanRfqk32BlW93IDlbCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:46.625112Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1632","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d86858161aa6d01c5769d09ad6c1196ff10c5a0039d19eca72a3688ab240f02","sha256:f0c28412c0de8f0f35c9568c51a7236ec80c4d6aa1da91d843d627286faec4dd"],"state_sha256":"452c67d5e036ffb0158cc4c4491296d330c5f3eaeb8a986a643556d5fde6d068"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"94PlRdGUfuxPCSKXIaMd5or0lfmJluNe3ayJvIj2wT3jEvcwHPTwRXrptXo/Ayo8J5HSeMSbhGM6eTrhLHO/Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T10:45:17.946508Z","bundle_sha256":"c852474cf78686a2fc1946b4978f7901e4cdf4fa2a1b2c25ec766365584ce528"}}