{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:TKE2ZJ36DUAED5CW5HLHFDWIUC","short_pith_number":"pith:TKE2ZJ36","canonical_record":{"source":{"id":"1110.5851","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-10-26T17:30:57Z","cross_cats_sorted":["math.KT","math.NT"],"title_canon_sha256":"69e7111fbb36fdcca61049e7b6376bc64261c57de4dd7128dfb1ca87a6842bd9","abstract_canon_sha256":"6e7edf205201a0adc32fe32e1e2bb2f56efaefdff34ba9011d1508478995df64"},"schema_version":"1.0"},"canonical_sha256":"9a89aca77e1d0041f456e9d6728ec8a09099b69379c8f687976e25a429294e4e","source":{"kind":"arxiv","id":"1110.5851","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5851","created_at":"2026-05-18T04:03:42Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5851v2","created_at":"2026-05-18T04:03:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5851","created_at":"2026-05-18T04:03:42Z"},{"alias_kind":"pith_short_12","alias_value":"TKE2ZJ36DUAE","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TKE2ZJ36DUAED5CW","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TKE2ZJ36","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:TKE2ZJ36DUAED5CW5HLHFDWIUC","target":"record","payload":{"canonical_record":{"source":{"id":"1110.5851","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-10-26T17:30:57Z","cross_cats_sorted":["math.KT","math.NT"],"title_canon_sha256":"69e7111fbb36fdcca61049e7b6376bc64261c57de4dd7128dfb1ca87a6842bd9","abstract_canon_sha256":"6e7edf205201a0adc32fe32e1e2bb2f56efaefdff34ba9011d1508478995df64"},"schema_version":"1.0"},"canonical_sha256":"9a89aca77e1d0041f456e9d6728ec8a09099b69379c8f687976e25a429294e4e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:42.778429Z","signature_b64":"Q7JnLEd2/qcc9YJTGgvQgpAASQBBtBRBuaW1YP72DkCCfCpcg5dADhYSc7c1B6ovc4dsHvjeMyU9BkT9SsdNCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a89aca77e1d0041f456e9d6728ec8a09099b69379c8f687976e25a429294e4e","last_reissued_at":"2026-05-18T04:03:42.777871Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:42.777871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.5851","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":"2026-05-18T04:03:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dfxOInRLFC+04J9pi1hZyMhpVGYsuGiDmZMg4lrPX81EE8U4+dbZ6L5WN15CclUZJC0orEdyaAHU3gknE/hkCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T13:50:11.041346Z"},"content_sha256":"bd33dc9515e9a579f6f3e2cc16266fdb8c3fb972ad8194f7f23587bec684d96b","schema_version":"1.0","event_id":"sha256:bd33dc9515e9a579f6f3e2cc16266fdb8c3fb972ad8194f7f23587bec684d96b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:TKE2ZJ36DUAED5CW5HLHFDWIUC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"p-adic J-homomorphisms and a product formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.NT"],"primary_cat":"math.AT","authors_text":"Dustin Clausen","submitted_at":"2011-10-26T17:30:57Z","abstract_excerpt":"One-point compactification turns real vector spaces into spheres. In homotopy theory, this transformation gets encoded in a map called the \"real J-homomorphism\". Here we define and investigate p-adic J-homomorphisms, which sort of turn p-adic vector spaces into spheres. Our main theorem is a product formula for these J-homomorphisms, saying what happens when you start with a rational vector space. This formula specializes to Hilbert's version of the quadratic reciprocity law after applying second homotopy groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5851","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":"2026-05-18T04:03:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GBj17WHyfRV162ej33l0ogJhI2Il3AzazwCvb+nLP3EzxvHQ8Ftemmv4G/pKWBFNAOLq82ENedcmKj1v30c2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T13:50:11.041788Z"},"content_sha256":"9d9c7cce32d944920b638b2e06b6ae5e95cde2f92147659a7350f617cfa2335a","schema_version":"1.0","event_id":"sha256:9d9c7cce32d944920b638b2e06b6ae5e95cde2f92147659a7350f617cfa2335a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TKE2ZJ36DUAED5CW5HLHFDWIUC/bundle.json","state_url":"https://pith.science/pith/TKE2ZJ36DUAED5CW5HLHFDWIUC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TKE2ZJ36DUAED5CW5HLHFDWIUC/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":"2026-06-04T13:50:11Z","links":{"resolver":"https://pith.science/pith/TKE2ZJ36DUAED5CW5HLHFDWIUC","bundle":"https://pith.science/pith/TKE2ZJ36DUAED5CW5HLHFDWIUC/bundle.json","state":"https://pith.science/pith/TKE2ZJ36DUAED5CW5HLHFDWIUC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TKE2ZJ36DUAED5CW5HLHFDWIUC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TKE2ZJ36DUAED5CW5HLHFDWIUC","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":"6e7edf205201a0adc32fe32e1e2bb2f56efaefdff34ba9011d1508478995df64","cross_cats_sorted":["math.KT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-10-26T17:30:57Z","title_canon_sha256":"69e7111fbb36fdcca61049e7b6376bc64261c57de4dd7128dfb1ca87a6842bd9"},"schema_version":"1.0","source":{"id":"1110.5851","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5851","created_at":"2026-05-18T04:03:42Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5851v2","created_at":"2026-05-18T04:03:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5851","created_at":"2026-05-18T04:03:42Z"},{"alias_kind":"pith_short_12","alias_value":"TKE2ZJ36DUAE","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TKE2ZJ36DUAED5CW","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TKE2ZJ36","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:9d9c7cce32d944920b638b2e06b6ae5e95cde2f92147659a7350f617cfa2335a","target":"graph","created_at":"2026-05-18T04:03:42Z","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":"One-point compactification turns real vector spaces into spheres. In homotopy theory, this transformation gets encoded in a map called the \"real J-homomorphism\". Here we define and investigate p-adic J-homomorphisms, which sort of turn p-adic vector spaces into spheres. Our main theorem is a product formula for these J-homomorphisms, saying what happens when you start with a rational vector space. This formula specializes to Hilbert's version of the quadratic reciprocity law after applying second homotopy groups.","authors_text":"Dustin Clausen","cross_cats":["math.KT","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-10-26T17:30:57Z","title":"p-adic J-homomorphisms and a product formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5851","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:bd33dc9515e9a579f6f3e2cc16266fdb8c3fb972ad8194f7f23587bec684d96b","target":"record","created_at":"2026-05-18T04:03:42Z","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":"6e7edf205201a0adc32fe32e1e2bb2f56efaefdff34ba9011d1508478995df64","cross_cats_sorted":["math.KT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-10-26T17:30:57Z","title_canon_sha256":"69e7111fbb36fdcca61049e7b6376bc64261c57de4dd7128dfb1ca87a6842bd9"},"schema_version":"1.0","source":{"id":"1110.5851","kind":"arxiv","version":2}},"canonical_sha256":"9a89aca77e1d0041f456e9d6728ec8a09099b69379c8f687976e25a429294e4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a89aca77e1d0041f456e9d6728ec8a09099b69379c8f687976e25a429294e4e","first_computed_at":"2026-05-18T04:03:42.777871Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:42.777871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q7JnLEd2/qcc9YJTGgvQgpAASQBBtBRBuaW1YP72DkCCfCpcg5dADhYSc7c1B6ovc4dsHvjeMyU9BkT9SsdNCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:42.778429Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.5851","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd33dc9515e9a579f6f3e2cc16266fdb8c3fb972ad8194f7f23587bec684d96b","sha256:9d9c7cce32d944920b638b2e06b6ae5e95cde2f92147659a7350f617cfa2335a"],"state_sha256":"6000b48baed265120ad07cb477babea4926875c3bfe13b8367bc67d9d403a684"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6cVjB+78p3QBRTV+rxVSizFSYA8+cEl0tUAqr9qdnanLe8zce6S/1Qk+luDDw3Vzi1JFGkb4nQNAI+ErtBM0Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T13:50:11.043924Z","bundle_sha256":"b736ebb07274586c2bca61e9ff40ce20972022b876ea752c315984712dc7f7bb"}}