{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:BFDAZUJCUQJ56DKZLCRIA7ZDYT","short_pith_number":"pith:BFDAZUJC","canonical_record":{"source":{"id":"1503.07408","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-25T15:02:03Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"a6c9f6087105986233d94a664c0421c60f3c17278e654bf0e929985a92d38033","abstract_canon_sha256":"ce55c6740ccebdceb8ac28b39051ca1b0a6568c5ebdd8bf0e586e1cd0afd64f0"},"schema_version":"1.0"},"canonical_sha256":"09460cd122a413df0d5958a2807f23c4f6a4e3d4a53713746193b92e341708ab","source":{"kind":"arxiv","id":"1503.07408","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.07408","created_at":"2026-05-18T00:39:29Z"},{"alias_kind":"arxiv_version","alias_value":"1503.07408v2","created_at":"2026-05-18T00:39:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07408","created_at":"2026-05-18T00:39:29Z"},{"alias_kind":"pith_short_12","alias_value":"BFDAZUJCUQJ5","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BFDAZUJCUQJ56DKZ","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BFDAZUJC","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:BFDAZUJCUQJ56DKZLCRIA7ZDYT","target":"record","payload":{"canonical_record":{"source":{"id":"1503.07408","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-25T15:02:03Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"a6c9f6087105986233d94a664c0421c60f3c17278e654bf0e929985a92d38033","abstract_canon_sha256":"ce55c6740ccebdceb8ac28b39051ca1b0a6568c5ebdd8bf0e586e1cd0afd64f0"},"schema_version":"1.0"},"canonical_sha256":"09460cd122a413df0d5958a2807f23c4f6a4e3d4a53713746193b92e341708ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:29.264981Z","signature_b64":"sy3ckkMW18VJLTa7XultLgYtCj6dVtrfCXh0Ta9oKq1KGhfHgPiAbxWUfUffH7o9rb6OCwmmnMEJUrCAnvLKAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09460cd122a413df0d5958a2807f23c4f6a4e3d4a53713746193b92e341708ab","last_reissued_at":"2026-05-18T00:39:29.264406Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:29.264406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.07408","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":"2026-05-18T00:39:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X/82meRSPWHRHXU7CASee4AW6xXZmN1nt66BroZdQUyIhK6dhYjrXLvq+U3qatzK0SpN1nKZOZ2YYQLLxB/9Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:07:08.116645Z"},"content_sha256":"27aa64fd3b42b0d1f416700a1ea3736db3c328f86fbbde8d986e83a15d31ddbe","schema_version":"1.0","event_id":"sha256:27aa64fd3b42b0d1f416700a1ea3736db3c328f86fbbde8d986e83a15d31ddbe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:BFDAZUJCUQJ56DKZLCRIA7ZDYT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gluing Manifolds in the Cahiers Topos","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.DG","authors_text":"Vincent S. Schlegel","submitted_at":"2015-03-25T15:02:03Z","abstract_excerpt":"We show that there is a fully faithful embedding of the category of manifolds with corners into the Cahiers topos, one of the premier models for Synthetic Differential Geometry. This embedding is shown to have a number of nice properties, such as preservation of open covers and transverse fibre products.\n  We develop a theory for gluing manifolds with corners in the Cahiers topos. In this setting, the result of gluing together manifolds with corners along a common face is shown to coincide with a pushout along an infinitesimally thickened face. Our theory is designed with a view toward future "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07408","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":"2026-05-18T00:39:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qbmNzduM5WBi9XWdiNG4P8HqPXNAOj6tC1S99nCNmzdbGu2A/Jxotx5013fOXMTsrNVzYn9HSXxBYCSgkBxrDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:07:08.117393Z"},"content_sha256":"21797e3995cfd3212280eae238b6f7a945600bc9125d1a70df76ced49ce589e9","schema_version":"1.0","event_id":"sha256:21797e3995cfd3212280eae238b6f7a945600bc9125d1a70df76ced49ce589e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BFDAZUJCUQJ56DKZLCRIA7ZDYT/bundle.json","state_url":"https://pith.science/pith/BFDAZUJCUQJ56DKZLCRIA7ZDYT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BFDAZUJCUQJ56DKZLCRIA7ZDYT/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":"2026-06-08T19:07:08Z","links":{"resolver":"https://pith.science/pith/BFDAZUJCUQJ56DKZLCRIA7ZDYT","bundle":"https://pith.science/pith/BFDAZUJCUQJ56DKZLCRIA7ZDYT/bundle.json","state":"https://pith.science/pith/BFDAZUJCUQJ56DKZLCRIA7ZDYT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BFDAZUJCUQJ56DKZLCRIA7ZDYT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BFDAZUJCUQJ56DKZLCRIA7ZDYT","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":"ce55c6740ccebdceb8ac28b39051ca1b0a6568c5ebdd8bf0e586e1cd0afd64f0","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-25T15:02:03Z","title_canon_sha256":"a6c9f6087105986233d94a664c0421c60f3c17278e654bf0e929985a92d38033"},"schema_version":"1.0","source":{"id":"1503.07408","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.07408","created_at":"2026-05-18T00:39:29Z"},{"alias_kind":"arxiv_version","alias_value":"1503.07408v2","created_at":"2026-05-18T00:39:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07408","created_at":"2026-05-18T00:39:29Z"},{"alias_kind":"pith_short_12","alias_value":"BFDAZUJCUQJ5","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BFDAZUJCUQJ56DKZ","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BFDAZUJC","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:21797e3995cfd3212280eae238b6f7a945600bc9125d1a70df76ced49ce589e9","target":"graph","created_at":"2026-05-18T00:39:29Z","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 show that there is a fully faithful embedding of the category of manifolds with corners into the Cahiers topos, one of the premier models for Synthetic Differential Geometry. This embedding is shown to have a number of nice properties, such as preservation of open covers and transverse fibre products.\n  We develop a theory for gluing manifolds with corners in the Cahiers topos. In this setting, the result of gluing together manifolds with corners along a common face is shown to coincide with a pushout along an infinitesimally thickened face. Our theory is designed with a view toward future ","authors_text":"Vincent S. Schlegel","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-25T15:02:03Z","title":"Gluing Manifolds in the Cahiers Topos"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07408","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":"sha256:27aa64fd3b42b0d1f416700a1ea3736db3c328f86fbbde8d986e83a15d31ddbe","target":"record","created_at":"2026-05-18T00:39:29Z","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":"ce55c6740ccebdceb8ac28b39051ca1b0a6568c5ebdd8bf0e586e1cd0afd64f0","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-25T15:02:03Z","title_canon_sha256":"a6c9f6087105986233d94a664c0421c60f3c17278e654bf0e929985a92d38033"},"schema_version":"1.0","source":{"id":"1503.07408","kind":"arxiv","version":2}},"canonical_sha256":"09460cd122a413df0d5958a2807f23c4f6a4e3d4a53713746193b92e341708ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09460cd122a413df0d5958a2807f23c4f6a4e3d4a53713746193b92e341708ab","first_computed_at":"2026-05-18T00:39:29.264406Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:29.264406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sy3ckkMW18VJLTa7XultLgYtCj6dVtrfCXh0Ta9oKq1KGhfHgPiAbxWUfUffH7o9rb6OCwmmnMEJUrCAnvLKAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:29.264981Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.07408","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27aa64fd3b42b0d1f416700a1ea3736db3c328f86fbbde8d986e83a15d31ddbe","sha256:21797e3995cfd3212280eae238b6f7a945600bc9125d1a70df76ced49ce589e9"],"state_sha256":"b00488cc3bfbeec409b43c439cbcb0b51e72f2de1fb9a924edfd6432b716a21b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e5Kfc0m2dIPg/pwAhWb6MS3UIIKwWPdsAGAn1PePeIycx/Mqo+fG3livrgfYCKkzL11KuhSjN4/SYWxa5dyKAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T19:07:08.121445Z","bundle_sha256":"087a0ad65aca1d5e804eb741939635ecfb4b94faf0ca15a7b3cd0c94c9ab8785"}}