{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:BX2J62GWVMRKY6AF4Y6SCE7S42","short_pith_number":"pith:BX2J62GW","canonical_record":{"source":{"id":"1512.01011","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2015-12-03T09:42:20Z","cross_cats_sorted":["math.DG","math.NT"],"title_canon_sha256":"da31957081342a2a9a57b37601dbaa1cf60cbba3698e51752e24058a396fb64d","abstract_canon_sha256":"bc00e328d737a989f73c04af4060a65e190f4686466e857ce70603a15623147d"},"schema_version":"1.0"},"canonical_sha256":"0df49f68d6ab22ac7805e63d2113f2e6b619712e504b5b798ada512177595c34","source":{"kind":"arxiv","id":"1512.01011","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01011","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01011v3","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01011","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"BX2J62GWVMRK","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BX2J62GWVMRKY6AF","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BX2J62GW","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:BX2J62GWVMRKY6AF4Y6SCE7S42","target":"record","payload":{"canonical_record":{"source":{"id":"1512.01011","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2015-12-03T09:42:20Z","cross_cats_sorted":["math.DG","math.NT"],"title_canon_sha256":"da31957081342a2a9a57b37601dbaa1cf60cbba3698e51752e24058a396fb64d","abstract_canon_sha256":"bc00e328d737a989f73c04af4060a65e190f4686466e857ce70603a15623147d"},"schema_version":"1.0"},"canonical_sha256":"0df49f68d6ab22ac7805e63d2113f2e6b619712e504b5b798ada512177595c34","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:46.717274Z","signature_b64":"Yecx5sbmwxx82LjhShA06UK4gbEYfZkwp2fXQI7Qgca4KoJDVJFqmgE5KDZ23OPhJJfs41dDFVUToy3BAlRkDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0df49f68d6ab22ac7805e63d2113f2e6b619712e504b5b798ada512177595c34","last_reissued_at":"2026-05-18T00:38:46.716652Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:46.716652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.01011","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":"2026-05-18T00:38:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xYHobQfLktV+fD6/14b/1+Ib/li6NQkN6y3EwzobwO7V5xLxxr8PRxgar1XuG2a2PTcn5mvpw7KAKS1qwElXBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:52:38.892728Z"},"content_sha256":"e079dc2fbf9de817029596f483d78cd5e01ef6f1b493f988c49c498b152f3cda","schema_version":"1.0","event_id":"sha256:e079dc2fbf9de817029596f483d78cd5e01ef6f1b493f988c49c498b152f3cda"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:BX2J62GWVMRKY6AF4Y6SCE7S42","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transcendental Hodge algebra","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.DG","math.NT"],"primary_cat":"math.AG","authors_text":"Misha Verbitsky","submitted_at":"2015-12-03T09:42:20Z","abstract_excerpt":"The transcendental Hodge lattice of a projective manifold $M$ is the smallest Hodge substructure in $p$-th cohomology which contains all holomorphic $p$-forms. We prove that the direct sum of all transcendental Hodge lattices has a natural algebraic structure, and compute this algebra explicitly for a hyperkahler manifold. As an application, we obtain a theorem about dimension of a compact torus $T$ admitting a symplectic embedding to a hyperkahler manifold $M$. If $M$ is generic in a $d$-dimensional family of deformations, then $\\dim T\\geq 2^{[(d+1)/2]}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01011","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":"2026-05-18T00:38:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PVdk3jJhX1vYRxeJon48dS9De1gI/28g7Olt2/CfQDeUVHQylT5K6C6m80g8QTqhiGYv06qA4QZfBNBmFW6EAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:52:38.893076Z"},"content_sha256":"09731888acc20ec04a467e8038d756a4a030b8505cdd01747f744a5dbd00f327","schema_version":"1.0","event_id":"sha256:09731888acc20ec04a467e8038d756a4a030b8505cdd01747f744a5dbd00f327"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BX2J62GWVMRKY6AF4Y6SCE7S42/bundle.json","state_url":"https://pith.science/pith/BX2J62GWVMRKY6AF4Y6SCE7S42/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BX2J62GWVMRKY6AF4Y6SCE7S42/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":"2026-06-02T02:52:38Z","links":{"resolver":"https://pith.science/pith/BX2J62GWVMRKY6AF4Y6SCE7S42","bundle":"https://pith.science/pith/BX2J62GWVMRKY6AF4Y6SCE7S42/bundle.json","state":"https://pith.science/pith/BX2J62GWVMRKY6AF4Y6SCE7S42/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BX2J62GWVMRKY6AF4Y6SCE7S42/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BX2J62GWVMRKY6AF4Y6SCE7S42","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":"bc00e328d737a989f73c04af4060a65e190f4686466e857ce70603a15623147d","cross_cats_sorted":["math.DG","math.NT"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2015-12-03T09:42:20Z","title_canon_sha256":"da31957081342a2a9a57b37601dbaa1cf60cbba3698e51752e24058a396fb64d"},"schema_version":"1.0","source":{"id":"1512.01011","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01011","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01011v3","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01011","created_at":"2026-05-18T00:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"BX2J62GWVMRK","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BX2J62GWVMRKY6AF","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BX2J62GW","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:09731888acc20ec04a467e8038d756a4a030b8505cdd01747f744a5dbd00f327","target":"graph","created_at":"2026-05-18T00:38:46Z","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":"The transcendental Hodge lattice of a projective manifold $M$ is the smallest Hodge substructure in $p$-th cohomology which contains all holomorphic $p$-forms. We prove that the direct sum of all transcendental Hodge lattices has a natural algebraic structure, and compute this algebra explicitly for a hyperkahler manifold. As an application, we obtain a theorem about dimension of a compact torus $T$ admitting a symplectic embedding to a hyperkahler manifold $M$. If $M$ is generic in a $d$-dimensional family of deformations, then $\\dim T\\geq 2^{[(d+1)/2]}$.","authors_text":"Misha Verbitsky","cross_cats":["math.DG","math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2015-12-03T09:42:20Z","title":"Transcendental Hodge algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01011","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:e079dc2fbf9de817029596f483d78cd5e01ef6f1b493f988c49c498b152f3cda","target":"record","created_at":"2026-05-18T00:38:46Z","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":"bc00e328d737a989f73c04af4060a65e190f4686466e857ce70603a15623147d","cross_cats_sorted":["math.DG","math.NT"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2015-12-03T09:42:20Z","title_canon_sha256":"da31957081342a2a9a57b37601dbaa1cf60cbba3698e51752e24058a396fb64d"},"schema_version":"1.0","source":{"id":"1512.01011","kind":"arxiv","version":3}},"canonical_sha256":"0df49f68d6ab22ac7805e63d2113f2e6b619712e504b5b798ada512177595c34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0df49f68d6ab22ac7805e63d2113f2e6b619712e504b5b798ada512177595c34","first_computed_at":"2026-05-18T00:38:46.716652Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:46.716652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yecx5sbmwxx82LjhShA06UK4gbEYfZkwp2fXQI7Qgca4KoJDVJFqmgE5KDZ23OPhJJfs41dDFVUToy3BAlRkDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:46.717274Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01011","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e079dc2fbf9de817029596f483d78cd5e01ef6f1b493f988c49c498b152f3cda","sha256:09731888acc20ec04a467e8038d756a4a030b8505cdd01747f744a5dbd00f327"],"state_sha256":"4a3f094392cc7b919a28741c00d3c8ff5ec7f83e32cc6e2736d7c803c2efc7ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TRsFndCg4x/VWY0tJpn2270m+moRWVx4WJQfYlM7yyCpwnwcefEkpjY+Quz2+8xIPJ89jMMja+e+K/kbK7NrCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T02:52:38.895056Z","bundle_sha256":"7de9ac0191c18194ba65c23250d7bf9d6e7fcc6214cec8da5fb3bac605d73526"}}