{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:POTRXHKSM6KRMVP5AMHRHJDWKX","short_pith_number":"pith:POTRXHKS","canonical_record":{"source":{"id":"1801.04443","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-01-13T14:12:23Z","cross_cats_sorted":[],"title_canon_sha256":"a1ae9dbf16732afab3f0da569c43307f6465606e9f0ba129fcc6b5651146b45e","abstract_canon_sha256":"7daca5cbe326fe84f2507998ac742fb47f83fec108a872f95512944b3e3b7fe7"},"schema_version":"1.0"},"canonical_sha256":"7ba71b9d5267951655fd030f13a47655e6225938161cd933b3e1c700ccb9d010","source":{"kind":"arxiv","id":"1801.04443","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04443","created_at":"2026-05-17T23:54:07Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04443v3","created_at":"2026-05-17T23:54:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04443","created_at":"2026-05-17T23:54:07Z"},{"alias_kind":"pith_short_12","alias_value":"POTRXHKSM6KR","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"POTRXHKSM6KRMVP5","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"POTRXHKS","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:POTRXHKSM6KRMVP5AMHRHJDWKX","target":"record","payload":{"canonical_record":{"source":{"id":"1801.04443","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-01-13T14:12:23Z","cross_cats_sorted":[],"title_canon_sha256":"a1ae9dbf16732afab3f0da569c43307f6465606e9f0ba129fcc6b5651146b45e","abstract_canon_sha256":"7daca5cbe326fe84f2507998ac742fb47f83fec108a872f95512944b3e3b7fe7"},"schema_version":"1.0"},"canonical_sha256":"7ba71b9d5267951655fd030f13a47655e6225938161cd933b3e1c700ccb9d010","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:07.471880Z","signature_b64":"gQ07mi4+xNe5pXM+cbH9dde8zFHIIfZandFVGsZdNnFsW4tyTldlEfQ5EaU/4pycJ0UCl7yIPb2pgKh0vKO5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ba71b9d5267951655fd030f13a47655e6225938161cd933b3e1c700ccb9d010","last_reissued_at":"2026-05-17T23:54:07.471233Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:07.471233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.04443","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":"2026-05-17T23:54:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4pLhDC700FprBLWH0kNlsGmkHpYq1y7r7RtEminsoclAfT4f+NqQlJm3GulquQ6YqqvCeuYBT6ZmUElZfGOyBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:13:21.968155Z"},"content_sha256":"88154582c15ceccbd348b5efdc666d9e33a2b8d2b4bcbfc4913f7aae895454bd","schema_version":"1.0","event_id":"sha256:88154582c15ceccbd348b5efdc666d9e33a2b8d2b4bcbfc4913f7aae895454bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:POTRXHKSM6KRMVP5AMHRHJDWKX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$L^{2}$ harmonic forms on complete special holonomy manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Teng Huang","submitted_at":"2018-01-13T14:12:23Z","abstract_excerpt":"In this article, we consider $L^{2}$ harmonic forms on a complete non-compact Riemannian manifold $X$ with a nonzero parallel form $\\omega$. The main result is that if $(X,\\omega)$ is a complete $G_{2}$- ( or $Spin(7)$-) manifold with a $d$(linear) $G_{2}$- (or $Spin(7)$-) structure form $\\omega$, the $L^{2}$ harmonic $2$-forms on $X$ will be vanish. As an application, we prove that the instanton equation with square integrable curvature on $(X,\\omega)$ only has trivial solution. We would also consider the Hodge theory on the principal $G$-bundle $E$ over $(X,\\omega)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04443","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":"2026-05-17T23:54:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E/pdDooIgdf2eqD3h8w5Ni511jhIBX6vlYWd/+TgpREU3198VMNVvdHr9PNVEK2Ho7ITsXe4eLpT0iV8bKoSCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:13:21.968814Z"},"content_sha256":"b7ceb056b05dbe158d65399085dd7f61b10ec64bd39703421f9dc9ddd5c848ec","schema_version":"1.0","event_id":"sha256:b7ceb056b05dbe158d65399085dd7f61b10ec64bd39703421f9dc9ddd5c848ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/POTRXHKSM6KRMVP5AMHRHJDWKX/bundle.json","state_url":"https://pith.science/pith/POTRXHKSM6KRMVP5AMHRHJDWKX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/POTRXHKSM6KRMVP5AMHRHJDWKX/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":"2026-06-03T15:13:21Z","links":{"resolver":"https://pith.science/pith/POTRXHKSM6KRMVP5AMHRHJDWKX","bundle":"https://pith.science/pith/POTRXHKSM6KRMVP5AMHRHJDWKX/bundle.json","state":"https://pith.science/pith/POTRXHKSM6KRMVP5AMHRHJDWKX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/POTRXHKSM6KRMVP5AMHRHJDWKX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:POTRXHKSM6KRMVP5AMHRHJDWKX","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":"7daca5cbe326fe84f2507998ac742fb47f83fec108a872f95512944b3e3b7fe7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-01-13T14:12:23Z","title_canon_sha256":"a1ae9dbf16732afab3f0da569c43307f6465606e9f0ba129fcc6b5651146b45e"},"schema_version":"1.0","source":{"id":"1801.04443","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04443","created_at":"2026-05-17T23:54:07Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04443v3","created_at":"2026-05-17T23:54:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04443","created_at":"2026-05-17T23:54:07Z"},{"alias_kind":"pith_short_12","alias_value":"POTRXHKSM6KR","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"POTRXHKSM6KRMVP5","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"POTRXHKS","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:b7ceb056b05dbe158d65399085dd7f61b10ec64bd39703421f9dc9ddd5c848ec","target":"graph","created_at":"2026-05-17T23:54:07Z","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 this article, we consider $L^{2}$ harmonic forms on a complete non-compact Riemannian manifold $X$ with a nonzero parallel form $\\omega$. The main result is that if $(X,\\omega)$ is a complete $G_{2}$- ( or $Spin(7)$-) manifold with a $d$(linear) $G_{2}$- (or $Spin(7)$-) structure form $\\omega$, the $L^{2}$ harmonic $2$-forms on $X$ will be vanish. As an application, we prove that the instanton equation with square integrable curvature on $(X,\\omega)$ only has trivial solution. We would also consider the Hodge theory on the principal $G$-bundle $E$ over $(X,\\omega)$.","authors_text":"Teng Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-01-13T14:12:23Z","title":"$L^{2}$ harmonic forms on complete special holonomy manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04443","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":"sha256:88154582c15ceccbd348b5efdc666d9e33a2b8d2b4bcbfc4913f7aae895454bd","target":"record","created_at":"2026-05-17T23:54:07Z","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":"7daca5cbe326fe84f2507998ac742fb47f83fec108a872f95512944b3e3b7fe7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-01-13T14:12:23Z","title_canon_sha256":"a1ae9dbf16732afab3f0da569c43307f6465606e9f0ba129fcc6b5651146b45e"},"schema_version":"1.0","source":{"id":"1801.04443","kind":"arxiv","version":3}},"canonical_sha256":"7ba71b9d5267951655fd030f13a47655e6225938161cd933b3e1c700ccb9d010","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ba71b9d5267951655fd030f13a47655e6225938161cd933b3e1c700ccb9d010","first_computed_at":"2026-05-17T23:54:07.471233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:07.471233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gQ07mi4+xNe5pXM+cbH9dde8zFHIIfZandFVGsZdNnFsW4tyTldlEfQ5EaU/4pycJ0UCl7yIPb2pgKh0vKO5BQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:07.471880Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.04443","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88154582c15ceccbd348b5efdc666d9e33a2b8d2b4bcbfc4913f7aae895454bd","sha256:b7ceb056b05dbe158d65399085dd7f61b10ec64bd39703421f9dc9ddd5c848ec"],"state_sha256":"8a55c94095739482fe9983e1a33d818904538ff23abb919026935bd658b0fba2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uk1s49nLXLmRqx07P6/F6UjdRmEbS+qcNz511wl8tC/7L4Fy94zJwqCp1YrBPG6MocqxDg5mgQkT+q9SPp8cDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T15:13:21.971968Z","bundle_sha256":"c2fb0e01bee9a293cc9fa59c8915f13b129c1fc464a29eff3bb8d8e2717d63fa"}}