{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:D6DASEL7OYXBGEVEWPL4YVRZXP","short_pith_number":"pith:D6DASEL7","canonical_record":{"source":{"id":"1708.02904","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-08-09T16:55:41Z","cross_cats_sorted":[],"title_canon_sha256":"341a534205a93db42afdab2e7df5b069ac7654040a8f46f857629b240ae15e05","abstract_canon_sha256":"3e478387f4ff1b8b66bae9300b57f34a5c4dce65e8431c6ac47d2bf318aff5ee"},"schema_version":"1.0"},"canonical_sha256":"1f8609117f762e1312a4b3d7cc5639bbc78ccf6a5894d402d5a5461e1b9c49ae","source":{"kind":"arxiv","id":"1708.02904","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.02904","created_at":"2026-05-18T00:18:46Z"},{"alias_kind":"arxiv_version","alias_value":"1708.02904v2","created_at":"2026-05-18T00:18:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02904","created_at":"2026-05-18T00:18:46Z"},{"alias_kind":"pith_short_12","alias_value":"D6DASEL7OYXB","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"D6DASEL7OYXBGEVE","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"D6DASEL7","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:D6DASEL7OYXBGEVEWPL4YVRZXP","target":"record","payload":{"canonical_record":{"source":{"id":"1708.02904","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-08-09T16:55:41Z","cross_cats_sorted":[],"title_canon_sha256":"341a534205a93db42afdab2e7df5b069ac7654040a8f46f857629b240ae15e05","abstract_canon_sha256":"3e478387f4ff1b8b66bae9300b57f34a5c4dce65e8431c6ac47d2bf318aff5ee"},"schema_version":"1.0"},"canonical_sha256":"1f8609117f762e1312a4b3d7cc5639bbc78ccf6a5894d402d5a5461e1b9c49ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:46.318232Z","signature_b64":"ubHc6V+alAEH/l2C0K1pRvkVTogmihrmkwW6ha+jHLUGFvnt9C1+0kuRLLSxR/Hkk8eSSfjl/vPMFbp3/hEVCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f8609117f762e1312a4b3d7cc5639bbc78ccf6a5894d402d5a5461e1b9c49ae","last_reissued_at":"2026-05-18T00:18:46.317676Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:46.317676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.02904","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:18:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3ekhC8jZr5jnhRQb74M1UzTi/GKpFmfSCh9jShOQOfOo6/gMbj3QmmnOm3L0H1l6y04ceBh0z8x9IaFbloRZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:20:06.333224Z"},"content_sha256":"e606523d806a56b4948fa18e395f1e41391500ed285aaa957fdbf5d6e41b46e5","schema_version":"1.0","event_id":"sha256:e606523d806a56b4948fa18e395f1e41391500ed285aaa957fdbf5d6e41b46e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:D6DASEL7OYXBGEVEWPL4YVRZXP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chern's contribution to the Hopf problem: an exposition based on Bryant's paper","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Aleksy Tralle, Markus Upmeier","submitted_at":"2017-08-09T16:55:41Z","abstract_excerpt":"We give a comprehensive account of Chern's Theorem that S^6 admits no omega-compatible almost complex structures. No claim to originality is being made, as the paper is mostly an expanded version of material already in the literature. This article extends the talks that both authors gave in Marburg during the conference \"(Non)existence of complex structures on S^6\" in April 2017."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02904","kind":"arxiv","version":2},"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":"2026-05-18T00:18:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sXrNZfpiVj4Mo5SgIgBdj/q/qrRHqCLEVKK1l4c5dooIXcVHYcgIY2/4foJJd5dqMpgKHrBQEJB6bmwHsdFlCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:20:06.333771Z"},"content_sha256":"e0c400be0c365167cf7ab8a2f67f115e54a441072ed84b083bb45dd8c609f8f7","schema_version":"1.0","event_id":"sha256:e0c400be0c365167cf7ab8a2f67f115e54a441072ed84b083bb45dd8c609f8f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D6DASEL7OYXBGEVEWPL4YVRZXP/bundle.json","state_url":"https://pith.science/pith/D6DASEL7OYXBGEVEWPL4YVRZXP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D6DASEL7OYXBGEVEWPL4YVRZXP/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":"2026-05-31T23:20:06Z","links":{"resolver":"https://pith.science/pith/D6DASEL7OYXBGEVEWPL4YVRZXP","bundle":"https://pith.science/pith/D6DASEL7OYXBGEVEWPL4YVRZXP/bundle.json","state":"https://pith.science/pith/D6DASEL7OYXBGEVEWPL4YVRZXP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D6DASEL7OYXBGEVEWPL4YVRZXP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:D6DASEL7OYXBGEVEWPL4YVRZXP","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":"3e478387f4ff1b8b66bae9300b57f34a5c4dce65e8431c6ac47d2bf318aff5ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-08-09T16:55:41Z","title_canon_sha256":"341a534205a93db42afdab2e7df5b069ac7654040a8f46f857629b240ae15e05"},"schema_version":"1.0","source":{"id":"1708.02904","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.02904","created_at":"2026-05-18T00:18:46Z"},{"alias_kind":"arxiv_version","alias_value":"1708.02904v2","created_at":"2026-05-18T00:18:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02904","created_at":"2026-05-18T00:18:46Z"},{"alias_kind":"pith_short_12","alias_value":"D6DASEL7OYXB","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"D6DASEL7OYXBGEVE","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"D6DASEL7","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:e0c400be0c365167cf7ab8a2f67f115e54a441072ed84b083bb45dd8c609f8f7","target":"graph","created_at":"2026-05-18T00:18:46Z","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":"We give a comprehensive account of Chern's Theorem that S^6 admits no omega-compatible almost complex structures. No claim to originality is being made, as the paper is mostly an expanded version of material already in the literature. This article extends the talks that both authors gave in Marburg during the conference \"(Non)existence of complex structures on S^6\" in April 2017.","authors_text":"Aleksy Tralle, Markus Upmeier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-08-09T16:55:41Z","title":"Chern's contribution to the Hopf problem: an exposition based on Bryant's paper"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02904","kind":"arxiv","version":2},"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:e606523d806a56b4948fa18e395f1e41391500ed285aaa957fdbf5d6e41b46e5","target":"record","created_at":"2026-05-18T00:18:46Z","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":"3e478387f4ff1b8b66bae9300b57f34a5c4dce65e8431c6ac47d2bf318aff5ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-08-09T16:55:41Z","title_canon_sha256":"341a534205a93db42afdab2e7df5b069ac7654040a8f46f857629b240ae15e05"},"schema_version":"1.0","source":{"id":"1708.02904","kind":"arxiv","version":2}},"canonical_sha256":"1f8609117f762e1312a4b3d7cc5639bbc78ccf6a5894d402d5a5461e1b9c49ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f8609117f762e1312a4b3d7cc5639bbc78ccf6a5894d402d5a5461e1b9c49ae","first_computed_at":"2026-05-18T00:18:46.317676Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:46.317676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ubHc6V+alAEH/l2C0K1pRvkVTogmihrmkwW6ha+jHLUGFvnt9C1+0kuRLLSxR/Hkk8eSSfjl/vPMFbp3/hEVCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:46.318232Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.02904","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e606523d806a56b4948fa18e395f1e41391500ed285aaa957fdbf5d6e41b46e5","sha256:e0c400be0c365167cf7ab8a2f67f115e54a441072ed84b083bb45dd8c609f8f7"],"state_sha256":"6b329c8e59341fbb9087bbc9bb335e5ebbfd53bca2d5b8ca6805c01c1f6886a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WcmuIUVmKxvdlXZ6TvH1DaoVrEeG3D88SbqNuAdOtMLlD40bmEWFStFf8qBJwJkhN3xdJ3xI2aT1jcNrudgKDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:20:06.337626Z","bundle_sha256":"d3161fe5f1dea42ab36b68750fe96c2bd9bb276f48782a12d627e42b30452e48"}}