{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:JW4E4HAZ2E5S7N3BIXIQ4NZOHF","short_pith_number":"pith:JW4E4HAZ","schema_version":"1.0","canonical_sha256":"4db84e1c19d13b2fb76145d10e372e397941031a0ed5776ec9b1fad90ee022ac","source":{"kind":"arxiv","id":"1209.0276","version":2},"attestation_state":"computed","paper":{"title":"Explicit Chabauty-Kim theory for the thrice punctured line in depth two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Ishai Dan-Cohen, Stefan Wewers","submitted_at":"2012-09-03T09:03:24Z","abstract_excerpt":"Let $X= \\mathbb{P}^1 \\setminus \\{0,1,\\infty\\}$, and let $S$ denote a finite set of prime numbers. In an article of 2005, Minhyong Kim gave a new proof of Siegel's theorem for $X$: the set $X(\\mathbb{Z}[S^{-1}])$ of $S$-integral points of $X$ is finite. The proof relies on a `nonabelian' version of the classical Chabauty method. At its heart is a modular interpretation of unipotent $p$-adic Hodge theory, given by a tower of morphisms $h_n$ between certain $\\mathbb{Q}_p$-varieties. We set out to obtain a better understanding of $h_2$. Its mysterious piece is a polynomial in $2|S|$ variables. Our"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1209.0276","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-09-03T09:03:24Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"325fb439247845821c5d5a169480deb39e8d6960608402a471fae53c554d3e40","abstract_canon_sha256":"dbb90f5f7eb4de05b1ef9f1275433bf8e6fd32f1a863b5beb43107ed6a7a758c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:30.277553Z","signature_b64":"HOn0cZkhp2Z6/Cpd+POnmw+CcQwR6uO26uoSNuY+WQiIrA1t49S5gkE+dpUYVOBjdvN9RhXWSVuKmJZ5WkPKBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4db84e1c19d13b2fb76145d10e372e397941031a0ed5776ec9b1fad90ee022ac","last_reissued_at":"2026-05-18T00:44:30.276984Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:30.276984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Explicit Chabauty-Kim theory for the thrice punctured line in depth two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Ishai Dan-Cohen, Stefan Wewers","submitted_at":"2012-09-03T09:03:24Z","abstract_excerpt":"Let $X= \\mathbb{P}^1 \\setminus \\{0,1,\\infty\\}$, and let $S$ denote a finite set of prime numbers. In an article of 2005, Minhyong Kim gave a new proof of Siegel's theorem for $X$: the set $X(\\mathbb{Z}[S^{-1}])$ of $S$-integral points of $X$ is finite. The proof relies on a `nonabelian' version of the classical Chabauty method. At its heart is a modular interpretation of unipotent $p$-adic Hodge theory, given by a tower of morphisms $h_n$ between certain $\\mathbb{Q}_p$-varieties. We set out to obtain a better understanding of $h_2$. Its mysterious piece is a polynomial in $2|S|$ variables. Our"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0276","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1209.0276","created_at":"2026-05-18T00:44:30.277074+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.0276v2","created_at":"2026-05-18T00:44:30.277074+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0276","created_at":"2026-05-18T00:44:30.277074+00:00"},{"alias_kind":"pith_short_12","alias_value":"JW4E4HAZ2E5S","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"JW4E4HAZ2E5S7N3B","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"JW4E4HAZ","created_at":"2026-05-18T12:27:11.947152+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JW4E4HAZ2E5S7N3BIXIQ4NZOHF","json":"https://pith.science/pith/JW4E4HAZ2E5S7N3BIXIQ4NZOHF.json","graph_json":"https://pith.science/api/pith-number/JW4E4HAZ2E5S7N3BIXIQ4NZOHF/graph.json","events_json":"https://pith.science/api/pith-number/JW4E4HAZ2E5S7N3BIXIQ4NZOHF/events.json","paper":"https://pith.science/paper/JW4E4HAZ"},"agent_actions":{"view_html":"https://pith.science/pith/JW4E4HAZ2E5S7N3BIXIQ4NZOHF","download_json":"https://pith.science/pith/JW4E4HAZ2E5S7N3BIXIQ4NZOHF.json","view_paper":"https://pith.science/paper/JW4E4HAZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.0276&json=true","fetch_graph":"https://pith.science/api/pith-number/JW4E4HAZ2E5S7N3BIXIQ4NZOHF/graph.json","fetch_events":"https://pith.science/api/pith-number/JW4E4HAZ2E5S7N3BIXIQ4NZOHF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JW4E4HAZ2E5S7N3BIXIQ4NZOHF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JW4E4HAZ2E5S7N3BIXIQ4NZOHF/action/storage_attestation","attest_author":"https://pith.science/pith/JW4E4HAZ2E5S7N3BIXIQ4NZOHF/action/author_attestation","sign_citation":"https://pith.science/pith/JW4E4HAZ2E5S7N3BIXIQ4NZOHF/action/citation_signature","submit_replication":"https://pith.science/pith/JW4E4HAZ2E5S7N3BIXIQ4NZOHF/action/replication_record"}},"created_at":"2026-05-18T00:44:30.277074+00:00","updated_at":"2026-05-18T00:44:30.277074+00:00"}