{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:YIFWZKX3ZTTTC7LBGY22HJQ4AG","short_pith_number":"pith:YIFWZKX3","canonical_record":{"source":{"id":"2503.12402","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-03-16T08:08:59Z","cross_cats_sorted":[],"title_canon_sha256":"3e27e22dd8322c9b6404a06e08b6070e91e20dcd7725d756d79baa09b0fd4f04","abstract_canon_sha256":"f7a82dd37b6d59f3d6cb5e2405c3a66fa2e700702bbd7204feae5d5a5cc60258"},"schema_version":"1.0"},"canonical_sha256":"c20b6caafbcce7317d613635a3a61c01999ad35d01cf494fd136859d37d8c628","source":{"kind":"arxiv","id":"2503.12402","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.12402","created_at":"2026-07-05T10:32:12Z"},{"alias_kind":"arxiv_version","alias_value":"2503.12402v1","created_at":"2026-07-05T10:32:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.12402","created_at":"2026-07-05T10:32:12Z"},{"alias_kind":"pith_short_12","alias_value":"YIFWZKX3ZTTT","created_at":"2026-07-05T10:32:12Z"},{"alias_kind":"pith_short_16","alias_value":"YIFWZKX3ZTTTC7LB","created_at":"2026-07-05T10:32:12Z"},{"alias_kind":"pith_short_8","alias_value":"YIFWZKX3","created_at":"2026-07-05T10:32:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:YIFWZKX3ZTTTC7LBGY22HJQ4AG","target":"record","payload":{"canonical_record":{"source":{"id":"2503.12402","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-03-16T08:08:59Z","cross_cats_sorted":[],"title_canon_sha256":"3e27e22dd8322c9b6404a06e08b6070e91e20dcd7725d756d79baa09b0fd4f04","abstract_canon_sha256":"f7a82dd37b6d59f3d6cb5e2405c3a66fa2e700702bbd7204feae5d5a5cc60258"},"schema_version":"1.0"},"canonical_sha256":"c20b6caafbcce7317d613635a3a61c01999ad35d01cf494fd136859d37d8c628","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:32:12.140473Z","signature_b64":"vbHxqg4B3qH/1s3QQJONs1RiSyFwtOZkQ6GtKeifFbkhop7vvw3Ym3gqs+JSSGuzGh1v4RBucJ4w+VUjfDFuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c20b6caafbcce7317d613635a3a61c01999ad35d01cf494fd136859d37d8c628","last_reissued_at":"2026-07-05T10:32:12.139787Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:32:12.139787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.12402","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":"2026-07-05T10:32:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vs6W1P69TyQqyR5VrUqv2Y6Hhxb6c/JEiDF+cgRybHeIbZTa19SsI7S33WgA8P/f0TnJ4CyXZSsTvThfdgErAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T01:16:16.165638Z"},"content_sha256":"5ad01742e7d24e5be29f269b7b6283dd5244dc82142bb479b0a0611a3e03c65c","schema_version":"1.0","event_id":"sha256:5ad01742e7d24e5be29f269b7b6283dd5244dc82142bb479b0a0611a3e03c65c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:YIFWZKX3ZTTTC7LBGY22HJQ4AG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A calibration in $\\mathbf R^{16}$ and Federer's product question","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Roger Z\\\"ust","submitted_at":"2025-03-16T08:08:59Z","abstract_excerpt":"Building upon the construction of a Cayley calibration adapted to a complex structure, we introduce a calibration $\\Phi$ in $\\bigwedge^8 \\mathbf R^{16}$ with $|\\Phi^2| = 294$. This enables us to show that the product of two orthogonally supported calibrations is not necessarily a calibration, thereby providing a negative answer to a question posed by Federer. Dadok and Harvey developed a general method for constructing calibrations as outer products of two unit spinors in the Clifford algebra. We show that $\\Phi$ arises from the product of two spinors with norm $1$ and $\\sqrt{2}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.12402","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.12402/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:32:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iAcf06t/NEmE5LPGZsOQ3BeAAKi4aj05xBtzBtDJJckbd3XzRdDGcreGPMTkvkWnMWyke9woKlCq9izF0G9EAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T01:16:16.166144Z"},"content_sha256":"2bd1f6294de7de85d1be6f65cd37aadd93c6a8141c53e4fa97bff4f6fad4a42b","schema_version":"1.0","event_id":"sha256:2bd1f6294de7de85d1be6f65cd37aadd93c6a8141c53e4fa97bff4f6fad4a42b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YIFWZKX3ZTTTC7LBGY22HJQ4AG/bundle.json","state_url":"https://pith.science/pith/YIFWZKX3ZTTTC7LBGY22HJQ4AG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YIFWZKX3ZTTTC7LBGY22HJQ4AG/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":"2026-08-21T01:16:16Z","links":{"resolver":"https://pith.science/pith/YIFWZKX3ZTTTC7LBGY22HJQ4AG","bundle":"https://pith.science/pith/YIFWZKX3ZTTTC7LBGY22HJQ4AG/bundle.json","state":"https://pith.science/pith/YIFWZKX3ZTTTC7LBGY22HJQ4AG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YIFWZKX3ZTTTC7LBGY22HJQ4AG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:YIFWZKX3ZTTTC7LBGY22HJQ4AG","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":"f7a82dd37b6d59f3d6cb5e2405c3a66fa2e700702bbd7204feae5d5a5cc60258","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-03-16T08:08:59Z","title_canon_sha256":"3e27e22dd8322c9b6404a06e08b6070e91e20dcd7725d756d79baa09b0fd4f04"},"schema_version":"1.0","source":{"id":"2503.12402","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.12402","created_at":"2026-07-05T10:32:12Z"},{"alias_kind":"arxiv_version","alias_value":"2503.12402v1","created_at":"2026-07-05T10:32:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.12402","created_at":"2026-07-05T10:32:12Z"},{"alias_kind":"pith_short_12","alias_value":"YIFWZKX3ZTTT","created_at":"2026-07-05T10:32:12Z"},{"alias_kind":"pith_short_16","alias_value":"YIFWZKX3ZTTTC7LB","created_at":"2026-07-05T10:32:12Z"},{"alias_kind":"pith_short_8","alias_value":"YIFWZKX3","created_at":"2026-07-05T10:32:12Z"}],"graph_snapshots":[{"event_id":"sha256:2bd1f6294de7de85d1be6f65cd37aadd93c6a8141c53e4fa97bff4f6fad4a42b","target":"graph","created_at":"2026-07-05T10:32:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2503.12402/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Building upon the construction of a Cayley calibration adapted to a complex structure, we introduce a calibration $\\Phi$ in $\\bigwedge^8 \\mathbf R^{16}$ with $|\\Phi^2| = 294$. This enables us to show that the product of two orthogonally supported calibrations is not necessarily a calibration, thereby providing a negative answer to a question posed by Federer. Dadok and Harvey developed a general method for constructing calibrations as outer products of two unit spinors in the Clifford algebra. We show that $\\Phi$ arises from the product of two spinors with norm $1$ and $\\sqrt{2}$.","authors_text":"Roger Z\\\"ust","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-03-16T08:08:59Z","title":"A calibration in $\\mathbf R^{16}$ and Federer's product question"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.12402","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":"sha256:5ad01742e7d24e5be29f269b7b6283dd5244dc82142bb479b0a0611a3e03c65c","target":"record","created_at":"2026-07-05T10:32:12Z","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":"f7a82dd37b6d59f3d6cb5e2405c3a66fa2e700702bbd7204feae5d5a5cc60258","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-03-16T08:08:59Z","title_canon_sha256":"3e27e22dd8322c9b6404a06e08b6070e91e20dcd7725d756d79baa09b0fd4f04"},"schema_version":"1.0","source":{"id":"2503.12402","kind":"arxiv","version":1}},"canonical_sha256":"c20b6caafbcce7317d613635a3a61c01999ad35d01cf494fd136859d37d8c628","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c20b6caafbcce7317d613635a3a61c01999ad35d01cf494fd136859d37d8c628","first_computed_at":"2026-07-05T10:32:12.139787Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:32:12.139787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vbHxqg4B3qH/1s3QQJONs1RiSyFwtOZkQ6GtKeifFbkhop7vvw3Ym3gqs+JSSGuzGh1v4RBucJ4w+VUjfDFuCw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:32:12.140473Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.12402","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ad01742e7d24e5be29f269b7b6283dd5244dc82142bb479b0a0611a3e03c65c","sha256:2bd1f6294de7de85d1be6f65cd37aadd93c6a8141c53e4fa97bff4f6fad4a42b"],"state_sha256":"a6214e89016d9b55707a03efafe53203a4c13d63d5a500e2fe8a5b32e4944de2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2xfFPzCd3YEvg4uVjXcBQ9whC+xfFLnGazaOg7jukS3iogXsbsSpPdXJO0T9oP76HLV81d/Noj6QWxc7n+p3DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T01:16:16.171536Z","bundle_sha256":"07a05b1c8e0c5f36096bbddbe40194a184912c1d983213de18c3f31e4152de20"}}