{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:3AG3KVBKADYSZSVR5WUXD23MMZ","short_pith_number":"pith:3AG3KVBK","canonical_record":{"source":{"id":"2606.23906","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-22T20:09:28Z","cross_cats_sorted":["math.AT","math.CT"],"title_canon_sha256":"2f839cd7f19cf4482822c1894bdd53c9ad242d3f89871b2c3926f7b67fc74bbd","abstract_canon_sha256":"a609d667e0f62b92686806f4f1d7e858c00d2e2a75db4ec28487cf2fbcea9f4a"},"schema_version":"1.0"},"canonical_sha256":"d80db5542a00f12ccab1eda971eb6c667b6a6c5e0fb4b418f548cbd2340da6c9","source":{"kind":"arxiv","id":"2606.23906","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23906","created_at":"2026-06-24T00:14:29Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23906v1","created_at":"2026-06-24T00:14:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23906","created_at":"2026-06-24T00:14:29Z"},{"alias_kind":"pith_short_12","alias_value":"3AG3KVBKADYS","created_at":"2026-06-24T00:14:29Z"},{"alias_kind":"pith_short_16","alias_value":"3AG3KVBKADYSZSVR","created_at":"2026-06-24T00:14:29Z"},{"alias_kind":"pith_short_8","alias_value":"3AG3KVBK","created_at":"2026-06-24T00:14:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:3AG3KVBKADYSZSVR5WUXD23MMZ","target":"record","payload":{"canonical_record":{"source":{"id":"2606.23906","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-22T20:09:28Z","cross_cats_sorted":["math.AT","math.CT"],"title_canon_sha256":"2f839cd7f19cf4482822c1894bdd53c9ad242d3f89871b2c3926f7b67fc74bbd","abstract_canon_sha256":"a609d667e0f62b92686806f4f1d7e858c00d2e2a75db4ec28487cf2fbcea9f4a"},"schema_version":"1.0"},"canonical_sha256":"d80db5542a00f12ccab1eda971eb6c667b6a6c5e0fb4b418f548cbd2340da6c9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-24T00:14:29.847041Z","signature_b64":"WJRfKjfNMjTFw2kpMas+JrgdnSzc5gr57IWCy1+AB+e3CyXpvrfRlfNR4tUMcjPNQlEGEW4XQHAKK3/DB4BVBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d80db5542a00f12ccab1eda971eb6c667b6a6c5e0fb4b418f548cbd2340da6c9","last_reissued_at":"2026-06-24T00:14:29.846711Z","signature_status":"signed_v1","first_computed_at":"2026-06-24T00:14:29.846711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.23906","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":"2026-06-24T00:14:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GsRs9KfQHEeRE/FQVhhbBvRXHoNd9fG7G3bFtvkgdCPoghOqxwpvbXJiYJRDTXMlz5pxj94gzTKD5eHvpy9LCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T00:09:53.689108Z"},"content_sha256":"54ab512d4844b5653e605fc12e4ecb547380e28cf9520723e6e789537dbfe8a5","schema_version":"1.0","event_id":"sha256:54ab512d4844b5653e605fc12e4ecb547380e28cf9520723e6e789537dbfe8a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:3AG3KVBKADYSZSVR5WUXD23MMZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"\\'Etale Fundamental Groups -- a geometric and topological approach to fundamental groups in algebraic geometry","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT","math.CT"],"primary_cat":"math.AG","authors_text":"Loris De Vos","submitted_at":"2026-06-22T20:09:28Z","abstract_excerpt":"This thesis explores the notion of fundamental groups across three mathematical settings. We begin with the classical topological theory of covering spaces, highlighting its structural analogy with Galois theory. We then follow Grothendieck in transporting these ideas to algebraic geometry. The inadequacy of the Zariski topology motivates the \\'etale topology, from which the \\'etale fundamental group is constructed and compared to its topological counterpart via transcendental methods. Finally, we linearise the theory through Tannakian duality, where fundamental groups are recovered as automor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23906","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/2606.23906/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":"2026-06-24T00:14:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v/JvH9VZ7na6eJhGJeZcJiLKHDZw1LZyFLQI8IR2KdiH8ZeAUCgim/ldbX6hCv/igTWZP9m4M0d5Vj0xFQWVAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T00:09:53.689730Z"},"content_sha256":"dfc5a971f02923017e374d2d7e2d8f0b5523c89f28ea350d8f035e82833cbd94","schema_version":"1.0","event_id":"sha256:dfc5a971f02923017e374d2d7e2d8f0b5523c89f28ea350d8f035e82833cbd94"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3AG3KVBKADYSZSVR5WUXD23MMZ/bundle.json","state_url":"https://pith.science/pith/3AG3KVBKADYSZSVR5WUXD23MMZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3AG3KVBKADYSZSVR5WUXD23MMZ/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":"2026-07-02T00:09:53Z","links":{"resolver":"https://pith.science/pith/3AG3KVBKADYSZSVR5WUXD23MMZ","bundle":"https://pith.science/pith/3AG3KVBKADYSZSVR5WUXD23MMZ/bundle.json","state":"https://pith.science/pith/3AG3KVBKADYSZSVR5WUXD23MMZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3AG3KVBKADYSZSVR5WUXD23MMZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3AG3KVBKADYSZSVR5WUXD23MMZ","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":"a609d667e0f62b92686806f4f1d7e858c00d2e2a75db4ec28487cf2fbcea9f4a","cross_cats_sorted":["math.AT","math.CT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-22T20:09:28Z","title_canon_sha256":"2f839cd7f19cf4482822c1894bdd53c9ad242d3f89871b2c3926f7b67fc74bbd"},"schema_version":"1.0","source":{"id":"2606.23906","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23906","created_at":"2026-06-24T00:14:29Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23906v1","created_at":"2026-06-24T00:14:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23906","created_at":"2026-06-24T00:14:29Z"},{"alias_kind":"pith_short_12","alias_value":"3AG3KVBKADYS","created_at":"2026-06-24T00:14:29Z"},{"alias_kind":"pith_short_16","alias_value":"3AG3KVBKADYSZSVR","created_at":"2026-06-24T00:14:29Z"},{"alias_kind":"pith_short_8","alias_value":"3AG3KVBK","created_at":"2026-06-24T00:14:29Z"}],"graph_snapshots":[{"event_id":"sha256:dfc5a971f02923017e374d2d7e2d8f0b5523c89f28ea350d8f035e82833cbd94","target":"graph","created_at":"2026-06-24T00:14:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.23906/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This thesis explores the notion of fundamental groups across three mathematical settings. We begin with the classical topological theory of covering spaces, highlighting its structural analogy with Galois theory. We then follow Grothendieck in transporting these ideas to algebraic geometry. The inadequacy of the Zariski topology motivates the \\'etale topology, from which the \\'etale fundamental group is constructed and compared to its topological counterpart via transcendental methods. Finally, we linearise the theory through Tannakian duality, where fundamental groups are recovered as automor","authors_text":"Loris De Vos","cross_cats":["math.AT","math.CT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-22T20:09:28Z","title":"\\'Etale Fundamental Groups -- a geometric and topological approach to fundamental groups in algebraic geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23906","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":"sha256:54ab512d4844b5653e605fc12e4ecb547380e28cf9520723e6e789537dbfe8a5","target":"record","created_at":"2026-06-24T00:14:29Z","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":"a609d667e0f62b92686806f4f1d7e858c00d2e2a75db4ec28487cf2fbcea9f4a","cross_cats_sorted":["math.AT","math.CT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-22T20:09:28Z","title_canon_sha256":"2f839cd7f19cf4482822c1894bdd53c9ad242d3f89871b2c3926f7b67fc74bbd"},"schema_version":"1.0","source":{"id":"2606.23906","kind":"arxiv","version":1}},"canonical_sha256":"d80db5542a00f12ccab1eda971eb6c667b6a6c5e0fb4b418f548cbd2340da6c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d80db5542a00f12ccab1eda971eb6c667b6a6c5e0fb4b418f548cbd2340da6c9","first_computed_at":"2026-06-24T00:14:29.846711Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T00:14:29.846711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WJRfKjfNMjTFw2kpMas+JrgdnSzc5gr57IWCy1+AB+e3CyXpvrfRlfNR4tUMcjPNQlEGEW4XQHAKK3/DB4BVBA==","signature_status":"signed_v1","signed_at":"2026-06-24T00:14:29.847041Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.23906","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54ab512d4844b5653e605fc12e4ecb547380e28cf9520723e6e789537dbfe8a5","sha256:dfc5a971f02923017e374d2d7e2d8f0b5523c89f28ea350d8f035e82833cbd94"],"state_sha256":"5380a8b4c3f674515352d74fa190ce8006159430bd536459192c1b10b642f172"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AnwZohJitGF+dHdL23CSV210XQY8JB+YIZQb0M/TouDVhmqbRC030oItLRnRwOyMCTAn82sRIGelsZgT+c/nCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T00:09:53.692873Z","bundle_sha256":"006cb4cce65170d15dc208be54b73210d290ac7dd28c23512d51a8884ed5e205"}}