{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:5EJYFHA4PN4BMOF6AUATK3OYSU","short_pith_number":"pith:5EJYFHA4","canonical_record":{"source":{"id":"1111.4030","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-17T07:54:04Z","cross_cats_sorted":[],"title_canon_sha256":"66097ba0346135f7cf60c1d6c6edeca3dc29cfd9f98f0cc01a553e2a7eec3903","abstract_canon_sha256":"d80d6eba4beb27fc660b4628763fb447c55d5e109310b2e84fee376730c212f3"},"schema_version":"1.0"},"canonical_sha256":"e913829c1c7b781638be0501356dd8952817886fdc9deda5157fff031005fd5a","source":{"kind":"arxiv","id":"1111.4030","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4030","created_at":"2026-05-18T00:17:27Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4030v3","created_at":"2026-05-18T00:17:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4030","created_at":"2026-05-18T00:17:27Z"},{"alias_kind":"pith_short_12","alias_value":"5EJYFHA4PN4B","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5EJYFHA4PN4BMOF6","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5EJYFHA4","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:5EJYFHA4PN4BMOF6AUATK3OYSU","target":"record","payload":{"canonical_record":{"source":{"id":"1111.4030","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-17T07:54:04Z","cross_cats_sorted":[],"title_canon_sha256":"66097ba0346135f7cf60c1d6c6edeca3dc29cfd9f98f0cc01a553e2a7eec3903","abstract_canon_sha256":"d80d6eba4beb27fc660b4628763fb447c55d5e109310b2e84fee376730c212f3"},"schema_version":"1.0"},"canonical_sha256":"e913829c1c7b781638be0501356dd8952817886fdc9deda5157fff031005fd5a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:27.446941Z","signature_b64":"q3kfNRf1Kvem+JzTblWs2OzOCfVgvzFYhJc5T8cXR2jYeblGlhOXnIP/SN01WO58q8yr3KBNXXvaE6nu5+7WDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e913829c1c7b781638be0501356dd8952817886fdc9deda5157fff031005fd5a","last_reissued_at":"2026-05-18T00:17:27.446272Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:27.446272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.4030","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":"2026-05-18T00:17:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ac6SPCeAuHWPXU4awzS5kKvffRhxhSFcr87dF4kkKO0f6V+8jrTDSh8f0ZWerO6bmRvj+b3VZbNFZp4vjAHzAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:53:15.178100Z"},"content_sha256":"61061c9a737356deb8d31585103f7bba3292e4944641b86d4f98a3f12c08d318","schema_version":"1.0","event_id":"sha256:61061c9a737356deb8d31585103f7bba3292e4944641b86d4f98a3f12c08d318"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:5EJYFHA4PN4BMOF6AUATK3OYSU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial mappings into a Stiefel manifold and immersions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Iwona Krzy\\.zanowska, Zbigniew Szafraniec","submitted_at":"2011-11-17T07:54:04Z","abstract_excerpt":"For a polynomial mapping from S^{n-k} to the Stiefel manifold \\widetilde{V}_k(\\R^{n}), where n-k is even, there is presented an effective method of expressing the corresponding element of the homotopy group \\pi_{n-k}\\widetilde{V}_k(\\R^{n})\\simeq\\Z in terms of signatures of quadratic forms. There is also given a method of computing the intersection number for a polynomial immersion from S^m to \\R^{2m}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4030","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":"2026-05-18T00:17:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fqiz0b3FrGCUvSgCsJshRrTKhocAjEip+dfV8ZSj1hRIjRRcBCljmc1uYeDAEBE637w4Jhl3d/KJEM6Zi7a0Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:53:15.178463Z"},"content_sha256":"6e6086e6e35112376c0e52b787e0a3cd91e155073f0cf132ad754d08a10518da","schema_version":"1.0","event_id":"sha256:6e6086e6e35112376c0e52b787e0a3cd91e155073f0cf132ad754d08a10518da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5EJYFHA4PN4BMOF6AUATK3OYSU/bundle.json","state_url":"https://pith.science/pith/5EJYFHA4PN4BMOF6AUATK3OYSU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5EJYFHA4PN4BMOF6AUATK3OYSU/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":"2026-07-01T21:53:15Z","links":{"resolver":"https://pith.science/pith/5EJYFHA4PN4BMOF6AUATK3OYSU","bundle":"https://pith.science/pith/5EJYFHA4PN4BMOF6AUATK3OYSU/bundle.json","state":"https://pith.science/pith/5EJYFHA4PN4BMOF6AUATK3OYSU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5EJYFHA4PN4BMOF6AUATK3OYSU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5EJYFHA4PN4BMOF6AUATK3OYSU","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":"d80d6eba4beb27fc660b4628763fb447c55d5e109310b2e84fee376730c212f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-17T07:54:04Z","title_canon_sha256":"66097ba0346135f7cf60c1d6c6edeca3dc29cfd9f98f0cc01a553e2a7eec3903"},"schema_version":"1.0","source":{"id":"1111.4030","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4030","created_at":"2026-05-18T00:17:27Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4030v3","created_at":"2026-05-18T00:17:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4030","created_at":"2026-05-18T00:17:27Z"},{"alias_kind":"pith_short_12","alias_value":"5EJYFHA4PN4B","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5EJYFHA4PN4BMOF6","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5EJYFHA4","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:6e6086e6e35112376c0e52b787e0a3cd91e155073f0cf132ad754d08a10518da","target":"graph","created_at":"2026-05-18T00:17:27Z","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":"For a polynomial mapping from S^{n-k} to the Stiefel manifold \\widetilde{V}_k(\\R^{n}), where n-k is even, there is presented an effective method of expressing the corresponding element of the homotopy group \\pi_{n-k}\\widetilde{V}_k(\\R^{n})\\simeq\\Z in terms of signatures of quadratic forms. There is also given a method of computing the intersection number for a polynomial immersion from S^m to \\R^{2m}.","authors_text":"Iwona Krzy\\.zanowska, Zbigniew Szafraniec","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-17T07:54:04Z","title":"Polynomial mappings into a Stiefel manifold and immersions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4030","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":"sha256:61061c9a737356deb8d31585103f7bba3292e4944641b86d4f98a3f12c08d318","target":"record","created_at":"2026-05-18T00:17:27Z","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":"d80d6eba4beb27fc660b4628763fb447c55d5e109310b2e84fee376730c212f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-17T07:54:04Z","title_canon_sha256":"66097ba0346135f7cf60c1d6c6edeca3dc29cfd9f98f0cc01a553e2a7eec3903"},"schema_version":"1.0","source":{"id":"1111.4030","kind":"arxiv","version":3}},"canonical_sha256":"e913829c1c7b781638be0501356dd8952817886fdc9deda5157fff031005fd5a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e913829c1c7b781638be0501356dd8952817886fdc9deda5157fff031005fd5a","first_computed_at":"2026-05-18T00:17:27.446272Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:27.446272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q3kfNRf1Kvem+JzTblWs2OzOCfVgvzFYhJc5T8cXR2jYeblGlhOXnIP/SN01WO58q8yr3KBNXXvaE6nu5+7WDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:27.446941Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.4030","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61061c9a737356deb8d31585103f7bba3292e4944641b86d4f98a3f12c08d318","sha256:6e6086e6e35112376c0e52b787e0a3cd91e155073f0cf132ad754d08a10518da"],"state_sha256":"3fea1ad15f9ff7b44c34dabed6203cc320e636ca81986ef90ff6b1bdf9cb2e8d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XBy2PCsZ73LzlM6uVdfqgqCQIF0Ju1iPTrmb5SJzZFIKJmuiH5Vn06FDlyZDjUyXDfNggmmysfwXXePsL+nEDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T21:53:15.180488Z","bundle_sha256":"774b55dd7cf3d82a846faa7140c4025316b5df79b27114a3c0a75f762205bdde"}}