{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:7THESW25OQ43QPCK2E52TDFB25","short_pith_number":"pith:7THESW25","canonical_record":{"source":{"id":"math/0402372","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2004-02-23T17:23:08Z","cross_cats_sorted":[],"title_canon_sha256":"993417df2885f99e4aa7bf45512ce96176658f2a99a95754ce0e8c531490cf97","abstract_canon_sha256":"d2fd421f87cf0d84d2de35a19d1601d8f1203d89b81511c397ef409fc3d19770"},"schema_version":"1.0"},"canonical_sha256":"fcce495b5d7439b83c4ad13ba98ca1d77700135e57f944ff52234208bca9e8c9","source":{"kind":"arxiv","id":"math/0402372","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0402372","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0402372v1","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0402372","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"pith_short_12","alias_value":"7THESW25OQ43","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"7THESW25OQ43QPCK","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"7THESW25","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:7THESW25OQ43QPCK2E52TDFB25","target":"record","payload":{"canonical_record":{"source":{"id":"math/0402372","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2004-02-23T17:23:08Z","cross_cats_sorted":[],"title_canon_sha256":"993417df2885f99e4aa7bf45512ce96176658f2a99a95754ce0e8c531490cf97","abstract_canon_sha256":"d2fd421f87cf0d84d2de35a19d1601d8f1203d89b81511c397ef409fc3d19770"},"schema_version":"1.0"},"canonical_sha256":"fcce495b5d7439b83c4ad13ba98ca1d77700135e57f944ff52234208bca9e8c9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:00.163184Z","signature_b64":"9Z8NLUEKcxnBO7Oi8yWdyMJ1fvRel2OizZ65l90hY8w0GrJPvHJvIvoeTVRdOjEH97Bz6pFe3Bm6kH6vwVYUBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fcce495b5d7439b83c4ad13ba98ca1d77700135e57f944ff52234208bca9e8c9","last_reissued_at":"2026-05-18T02:38:00.162751Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:00.162751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0402372","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":"2026-05-18T02:38:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LSRZWIJrsohrM0BhRCVLL/j3z/rWVpl3NBluH0wXRcOOQR9mRn+2jAix7Wda9sKoG473Xv16vAvNf69NHjRFDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T17:00:04.031194Z"},"content_sha256":"ab97375e5976bda1c1ed76e6de89d9cc47c3164b0e0b0fc44070ef4dcbe72b98","schema_version":"1.0","event_id":"sha256:ab97375e5976bda1c1ed76e6de89d9cc47c3164b0e0b0fc44070ef4dcbe72b98"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:7THESW25OQ43QPCK2E52TDFB25","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Formal groups and stable homotopy of commutative rings","license":"","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Stefan Schwede","submitted_at":"2004-02-23T17:23:08Z","abstract_excerpt":"We explain a new relationship between formal group laws and ring spectra in stable homotopy theory. We study a ring spectrum denoted DB which depends on a commutative ring B and is closely related to the topological Andre-Quillen homology of B. We present an explicit construction which to every 1-dimensional and commutative formal group law F over B associates a morphism of ring spectra F_*: HZ --> DB from the Eilenberg-MacLane ring spectrum of the integers. We show that formal group laws account for all such ring spectrum maps, and we identify the space of ring spectrum maps between HZ and DB"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0402372","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":""},"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":"2026-05-18T02:38:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6+tqoVzF58NeLbSsdH7WWaF5DY94kj6lwmcyH5RJLk+CwwTrrARGMEJhXjCu0VBjMYEtBZdDialv7JcGt35mCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T17:00:04.031551Z"},"content_sha256":"9bd952e5d28647412a7cc1f1b7f0c7f65d7efebe7025a56dd7cf4cac7c877dec","schema_version":"1.0","event_id":"sha256:9bd952e5d28647412a7cc1f1b7f0c7f65d7efebe7025a56dd7cf4cac7c877dec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7THESW25OQ43QPCK2E52TDFB25/bundle.json","state_url":"https://pith.science/pith/7THESW25OQ43QPCK2E52TDFB25/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7THESW25OQ43QPCK2E52TDFB25/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":"2026-07-06T17:00:04Z","links":{"resolver":"https://pith.science/pith/7THESW25OQ43QPCK2E52TDFB25","bundle":"https://pith.science/pith/7THESW25OQ43QPCK2E52TDFB25/bundle.json","state":"https://pith.science/pith/7THESW25OQ43QPCK2E52TDFB25/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7THESW25OQ43QPCK2E52TDFB25/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:7THESW25OQ43QPCK2E52TDFB25","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":"d2fd421f87cf0d84d2de35a19d1601d8f1203d89b81511c397ef409fc3d19770","cross_cats_sorted":[],"license":"","primary_cat":"math.AT","submitted_at":"2004-02-23T17:23:08Z","title_canon_sha256":"993417df2885f99e4aa7bf45512ce96176658f2a99a95754ce0e8c531490cf97"},"schema_version":"1.0","source":{"id":"math/0402372","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0402372","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0402372v1","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0402372","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"pith_short_12","alias_value":"7THESW25OQ43","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"7THESW25OQ43QPCK","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"7THESW25","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:9bd952e5d28647412a7cc1f1b7f0c7f65d7efebe7025a56dd7cf4cac7c877dec","target":"graph","created_at":"2026-05-18T02:38:00Z","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 explain a new relationship between formal group laws and ring spectra in stable homotopy theory. We study a ring spectrum denoted DB which depends on a commutative ring B and is closely related to the topological Andre-Quillen homology of B. We present an explicit construction which to every 1-dimensional and commutative formal group law F over B associates a morphism of ring spectra F_*: HZ --> DB from the Eilenberg-MacLane ring spectrum of the integers. We show that formal group laws account for all such ring spectrum maps, and we identify the space of ring spectrum maps between HZ and DB","authors_text":"Stefan Schwede","cross_cats":[],"headline":"","license":"","primary_cat":"math.AT","submitted_at":"2004-02-23T17:23:08Z","title":"Formal groups and stable homotopy of commutative rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0402372","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:ab97375e5976bda1c1ed76e6de89d9cc47c3164b0e0b0fc44070ef4dcbe72b98","target":"record","created_at":"2026-05-18T02:38:00Z","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":"d2fd421f87cf0d84d2de35a19d1601d8f1203d89b81511c397ef409fc3d19770","cross_cats_sorted":[],"license":"","primary_cat":"math.AT","submitted_at":"2004-02-23T17:23:08Z","title_canon_sha256":"993417df2885f99e4aa7bf45512ce96176658f2a99a95754ce0e8c531490cf97"},"schema_version":"1.0","source":{"id":"math/0402372","kind":"arxiv","version":1}},"canonical_sha256":"fcce495b5d7439b83c4ad13ba98ca1d77700135e57f944ff52234208bca9e8c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fcce495b5d7439b83c4ad13ba98ca1d77700135e57f944ff52234208bca9e8c9","first_computed_at":"2026-05-18T02:38:00.162751Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:00.162751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9Z8NLUEKcxnBO7Oi8yWdyMJ1fvRel2OizZ65l90hY8w0GrJPvHJvIvoeTVRdOjEH97Bz6pFe3Bm6kH6vwVYUBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:00.163184Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0402372","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab97375e5976bda1c1ed76e6de89d9cc47c3164b0e0b0fc44070ef4dcbe72b98","sha256:9bd952e5d28647412a7cc1f1b7f0c7f65d7efebe7025a56dd7cf4cac7c877dec"],"state_sha256":"b40799875eadf747bb10c4c2d19bee335c41bfe33cd05862795e62d8a8ad3624"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YGGiGUd826FrRGyAJq0loWziWb3N/y7e/phaqI3z9V9nwxl1Nrn5HUay5/vwIFWrq/9x2kXvmUbVnJehyEIxAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T17:00:04.033491Z","bundle_sha256":"37823c3b070f192461a94b8827129b61aa25bd7e9a81219a08fca948b1d57813"}}