{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:2W3U2K5EOQBJX4SOY5LPXRPPBX","short_pith_number":"pith:2W3U2K5E","canonical_record":{"source":{"id":"1212.0029","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-11-30T22:35:04Z","cross_cats_sorted":[],"title_canon_sha256":"9ccb7591597cb0bd0a647d1fa0dcc80d9713890bcb29f0d9291b8dd76db0f987","abstract_canon_sha256":"bf181b9a5f84e2e4957f3c04748f4715c9a6e59303ace390d7a633a667013493"},"schema_version":"1.0"},"canonical_sha256":"d5b74d2ba474029bf24ec756fbc5ef0dfe81a5cfaf6f529436f6eaff607f673b","source":{"kind":"arxiv","id":"1212.0029","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0029","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0029v1","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0029","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"pith_short_12","alias_value":"2W3U2K5EOQBJ","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2W3U2K5EOQBJX4SO","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2W3U2K5E","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:2W3U2K5EOQBJX4SOY5LPXRPPBX","target":"record","payload":{"canonical_record":{"source":{"id":"1212.0029","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-11-30T22:35:04Z","cross_cats_sorted":[],"title_canon_sha256":"9ccb7591597cb0bd0a647d1fa0dcc80d9713890bcb29f0d9291b8dd76db0f987","abstract_canon_sha256":"bf181b9a5f84e2e4957f3c04748f4715c9a6e59303ace390d7a633a667013493"},"schema_version":"1.0"},"canonical_sha256":"d5b74d2ba474029bf24ec756fbc5ef0dfe81a5cfaf6f529436f6eaff607f673b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:27.599117Z","signature_b64":"HLxaJEF4TMqx3IwO2BPCOsZdvZZuU9NhyEayr9Uu7qSq7Q8rt1NK48vQS1PvBVXe4k3oO+GBCy14RjTbEETbBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5b74d2ba474029bf24ec756fbc5ef0dfe81a5cfaf6f529436f6eaff607f673b","last_reissued_at":"2026-05-18T03:39:27.598232Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:27.598232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.0029","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":"2026-05-18T03:39:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"06MEuG9RWVtFhFzW87ZgHMQ4WhxKZWt9ug0jGP3qoB750QZeRakK61ulWQMRk2W46VuwfwJu2yaaFZSjbLeLAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T21:53:55.433395Z"},"content_sha256":"cecb4f4585d2f6d9672e99b86d310c635391fb479f86f7e40c43945c0ebcb0a8","schema_version":"1.0","event_id":"sha256:cecb4f4585d2f6d9672e99b86d310c635391fb479f86f7e40c43945c0ebcb0a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:2W3U2K5EOQBJX4SOY5LPXRPPBX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Squares of positive $(p,p)$-forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Szymon Plis, Zbigniew Blocki","submitted_at":"2012-11-30T22:35:04Z","abstract_excerpt":"We show that if $\\alpha$ is a positive $(2,2)$-form then so is $\\alpha^2$. We also prove that this is no longer true for forms of higher degree."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0029","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":"2026-05-18T03:39:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p0cJKClxMre3p2OhF4fLcjxvKlN3ZhDkDBnVeQ0d2hgqB3U+JJuGJgdCyOZ2uIZhimWX4v1zFrnJNhrTjY7DDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T21:53:55.434107Z"},"content_sha256":"97d17b27450f117d93b3d493ccdda9483a287c26d15f5e7ddda43682c81e8c13","schema_version":"1.0","event_id":"sha256:97d17b27450f117d93b3d493ccdda9483a287c26d15f5e7ddda43682c81e8c13"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2W3U2K5EOQBJX4SOY5LPXRPPBX/bundle.json","state_url":"https://pith.science/pith/2W3U2K5EOQBJX4SOY5LPXRPPBX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2W3U2K5EOQBJX4SOY5LPXRPPBX/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":"2026-05-29T21:53:55Z","links":{"resolver":"https://pith.science/pith/2W3U2K5EOQBJX4SOY5LPXRPPBX","bundle":"https://pith.science/pith/2W3U2K5EOQBJX4SOY5LPXRPPBX/bundle.json","state":"https://pith.science/pith/2W3U2K5EOQBJX4SOY5LPXRPPBX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2W3U2K5EOQBJX4SOY5LPXRPPBX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2W3U2K5EOQBJX4SOY5LPXRPPBX","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":"bf181b9a5f84e2e4957f3c04748f4715c9a6e59303ace390d7a633a667013493","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-11-30T22:35:04Z","title_canon_sha256":"9ccb7591597cb0bd0a647d1fa0dcc80d9713890bcb29f0d9291b8dd76db0f987"},"schema_version":"1.0","source":{"id":"1212.0029","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0029","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0029v1","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0029","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"pith_short_12","alias_value":"2W3U2K5EOQBJ","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2W3U2K5EOQBJX4SO","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2W3U2K5E","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:97d17b27450f117d93b3d493ccdda9483a287c26d15f5e7ddda43682c81e8c13","target":"graph","created_at":"2026-05-18T03:39:27Z","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 show that if $\\alpha$ is a positive $(2,2)$-form then so is $\\alpha^2$. We also prove that this is no longer true for forms of higher degree.","authors_text":"Szymon Plis, Zbigniew Blocki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-11-30T22:35:04Z","title":"Squares of positive $(p,p)$-forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0029","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:cecb4f4585d2f6d9672e99b86d310c635391fb479f86f7e40c43945c0ebcb0a8","target":"record","created_at":"2026-05-18T03:39:27Z","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":"bf181b9a5f84e2e4957f3c04748f4715c9a6e59303ace390d7a633a667013493","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-11-30T22:35:04Z","title_canon_sha256":"9ccb7591597cb0bd0a647d1fa0dcc80d9713890bcb29f0d9291b8dd76db0f987"},"schema_version":"1.0","source":{"id":"1212.0029","kind":"arxiv","version":1}},"canonical_sha256":"d5b74d2ba474029bf24ec756fbc5ef0dfe81a5cfaf6f529436f6eaff607f673b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5b74d2ba474029bf24ec756fbc5ef0dfe81a5cfaf6f529436f6eaff607f673b","first_computed_at":"2026-05-18T03:39:27.598232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:27.598232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HLxaJEF4TMqx3IwO2BPCOsZdvZZuU9NhyEayr9Uu7qSq7Q8rt1NK48vQS1PvBVXe4k3oO+GBCy14RjTbEETbBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:27.599117Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.0029","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cecb4f4585d2f6d9672e99b86d310c635391fb479f86f7e40c43945c0ebcb0a8","sha256:97d17b27450f117d93b3d493ccdda9483a287c26d15f5e7ddda43682c81e8c13"],"state_sha256":"c5529362a8da2e4e842352beddfdb80c395525fba2a35b4af45f60199fafbd94"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qVA6m7edKcXnafGi2TazkjLPosd6k4fgvKjGYYfinYQiGNd3a43hVgYRLEnZ1CzMxiemIEOY/KQ66O9QdXxSCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T21:53:55.437943Z","bundle_sha256":"ec0a9bf38b6702bc1d0756e6f722d81223acb72afbce809ac9f94f3e32fb6427"}}