{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:K7UATSEUQDHA2O36HPS5BYRQQB","short_pith_number":"pith:K7UATSEU","canonical_record":{"source":{"id":"2410.02668","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-10-03T16:51:34Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"2df3bd780ec907d3e5a2f2d8753deaa0f37f2ed89b537bd65e5875d8afc45ecb","abstract_canon_sha256":"b1cbe841955228907710a51532a737fe886571ada8baa93e4b32b37ed3ac7028"},"schema_version":"1.0"},"canonical_sha256":"57e809c89480ce0d3b7e3be5d0e2308077e9748d064dafbb8a3aec2eb282e39a","source":{"kind":"arxiv","id":"2410.02668","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.02668","created_at":"2026-07-05T09:15:23Z"},{"alias_kind":"arxiv_version","alias_value":"2410.02668v1","created_at":"2026-07-05T09:15:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.02668","created_at":"2026-07-05T09:15:23Z"},{"alias_kind":"pith_short_12","alias_value":"K7UATSEUQDHA","created_at":"2026-07-05T09:15:23Z"},{"alias_kind":"pith_short_16","alias_value":"K7UATSEUQDHA2O36","created_at":"2026-07-05T09:15:23Z"},{"alias_kind":"pith_short_8","alias_value":"K7UATSEU","created_at":"2026-07-05T09:15:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:K7UATSEUQDHA2O36HPS5BYRQQB","target":"record","payload":{"canonical_record":{"source":{"id":"2410.02668","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-10-03T16:51:34Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"2df3bd780ec907d3e5a2f2d8753deaa0f37f2ed89b537bd65e5875d8afc45ecb","abstract_canon_sha256":"b1cbe841955228907710a51532a737fe886571ada8baa93e4b32b37ed3ac7028"},"schema_version":"1.0"},"canonical_sha256":"57e809c89480ce0d3b7e3be5d0e2308077e9748d064dafbb8a3aec2eb282e39a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:15:23.977853Z","signature_b64":"yZQY1EHVu7FXmD5r3F8K3RvIlC3q8StrHhlPAF9OaFW0LEHHLjQnEfFScdpfzLCxRRHTGD6D3IN6VvuuT5nYAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57e809c89480ce0d3b7e3be5d0e2308077e9748d064dafbb8a3aec2eb282e39a","last_reissued_at":"2026-07-05T09:15:23.977434Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:15:23.977434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.02668","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":"2026-07-05T09:15:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PKyVnmd42aCO486ScJGybP6DFD80Ix2vVEhV+IH5JUAFYkj4oXprTOoqtK1GPG/lxTSejnvWjdlNWS90MOUUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T06:39:02.590767Z"},"content_sha256":"0a575224a299cd9cca96fd650f82bc1e6f09c88be57cd97913f9fbde49413f2f","schema_version":"1.0","event_id":"sha256:0a575224a299cd9cca96fd650f82bc1e6f09c88be57cd97913f9fbde49413f2f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:K7UATSEUQDHA2O36HPS5BYRQQB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"There is no Cazanave's Theorem for punctured affine space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AT","authors_text":"Thomas Brazelton, William Hornslien","submitted_at":"2024-10-03T16:51:34Z","abstract_excerpt":"In his thesis, Cazanave proved that the set of naive $\\mathbb{A}^1$-homotopy classes of endomorphisms of the projective line admits a monoid structure whose group completion is genuine $\\mathbb{A}^1$-homotopy classes of endomorphisms of the projective line. In this very short note we show that such a statement is never true for punctured affine space $\\mathbb{A}^n\\setminus\\{0\\}$ for $n \\ge 2$ ."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.02668","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.02668/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:15:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dHD6tyIfJKGwQOz4huomrp83ZeNrzf+lH6QQmvLW3AdKdZZPvn0F+xTldf7dVDQHjFH0kb2s1evCmaY0+MhnAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T06:39:02.591696Z"},"content_sha256":"ec2a4116c44782f9a20c54a801f1d7dad089a7144e10f26a082f4773a25970a6","schema_version":"1.0","event_id":"sha256:ec2a4116c44782f9a20c54a801f1d7dad089a7144e10f26a082f4773a25970a6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K7UATSEUQDHA2O36HPS5BYRQQB/bundle.json","state_url":"https://pith.science/pith/K7UATSEUQDHA2O36HPS5BYRQQB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K7UATSEUQDHA2O36HPS5BYRQQB/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":"2026-07-07T06:39:02Z","links":{"resolver":"https://pith.science/pith/K7UATSEUQDHA2O36HPS5BYRQQB","bundle":"https://pith.science/pith/K7UATSEUQDHA2O36HPS5BYRQQB/bundle.json","state":"https://pith.science/pith/K7UATSEUQDHA2O36HPS5BYRQQB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K7UATSEUQDHA2O36HPS5BYRQQB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:K7UATSEUQDHA2O36HPS5BYRQQB","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":"b1cbe841955228907710a51532a737fe886571ada8baa93e4b32b37ed3ac7028","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-10-03T16:51:34Z","title_canon_sha256":"2df3bd780ec907d3e5a2f2d8753deaa0f37f2ed89b537bd65e5875d8afc45ecb"},"schema_version":"1.0","source":{"id":"2410.02668","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.02668","created_at":"2026-07-05T09:15:23Z"},{"alias_kind":"arxiv_version","alias_value":"2410.02668v1","created_at":"2026-07-05T09:15:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.02668","created_at":"2026-07-05T09:15:23Z"},{"alias_kind":"pith_short_12","alias_value":"K7UATSEUQDHA","created_at":"2026-07-05T09:15:23Z"},{"alias_kind":"pith_short_16","alias_value":"K7UATSEUQDHA2O36","created_at":"2026-07-05T09:15:23Z"},{"alias_kind":"pith_short_8","alias_value":"K7UATSEU","created_at":"2026-07-05T09:15:23Z"}],"graph_snapshots":[{"event_id":"sha256:ec2a4116c44782f9a20c54a801f1d7dad089a7144e10f26a082f4773a25970a6","target":"graph","created_at":"2026-07-05T09:15:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.02668/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In his thesis, Cazanave proved that the set of naive $\\mathbb{A}^1$-homotopy classes of endomorphisms of the projective line admits a monoid structure whose group completion is genuine $\\mathbb{A}^1$-homotopy classes of endomorphisms of the projective line. In this very short note we show that such a statement is never true for punctured affine space $\\mathbb{A}^n\\setminus\\{0\\}$ for $n \\ge 2$ .","authors_text":"Thomas Brazelton, William Hornslien","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-10-03T16:51:34Z","title":"There is no Cazanave's Theorem for punctured affine space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.02668","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":"sha256:0a575224a299cd9cca96fd650f82bc1e6f09c88be57cd97913f9fbde49413f2f","target":"record","created_at":"2026-07-05T09:15:23Z","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":"b1cbe841955228907710a51532a737fe886571ada8baa93e4b32b37ed3ac7028","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-10-03T16:51:34Z","title_canon_sha256":"2df3bd780ec907d3e5a2f2d8753deaa0f37f2ed89b537bd65e5875d8afc45ecb"},"schema_version":"1.0","source":{"id":"2410.02668","kind":"arxiv","version":1}},"canonical_sha256":"57e809c89480ce0d3b7e3be5d0e2308077e9748d064dafbb8a3aec2eb282e39a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57e809c89480ce0d3b7e3be5d0e2308077e9748d064dafbb8a3aec2eb282e39a","first_computed_at":"2026-07-05T09:15:23.977434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:15:23.977434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yZQY1EHVu7FXmD5r3F8K3RvIlC3q8StrHhlPAF9OaFW0LEHHLjQnEfFScdpfzLCxRRHTGD6D3IN6VvuuT5nYAg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:15:23.977853Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.02668","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a575224a299cd9cca96fd650f82bc1e6f09c88be57cd97913f9fbde49413f2f","sha256:ec2a4116c44782f9a20c54a801f1d7dad089a7144e10f26a082f4773a25970a6"],"state_sha256":"5a8b5066ace9658c609562a68a696bd06bf2ff0eafb35d6f34efadd9a790f2ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VughmVB6WGlYzQcjWsl7be20EzFGo5FebdHGC8BZp+DYtF9w/0Ldl3PjMjB5EDD+XSXJXnaH8VAoJYhfFMsUDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T06:39:02.594956Z","bundle_sha256":"041cb151218677cf580abda5a0c682ee2bf17c7d50f75dcca9fc1b1a086076ad"}}