{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:X7NGKH25USZGESZTLSBM4DCT62","short_pith_number":"pith:X7NGKH25","schema_version":"1.0","canonical_sha256":"bfda651f5da4b2624b335c82ce0c53f6bd817add3328182745b9a90bac1361a7","source":{"kind":"arxiv","id":"1007.0511","version":2},"attestation_state":"computed","paper":{"title":"Tropical Geometry and the Motivic Nearby Fiber","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Alan Stapledon, Eric Katz","submitted_at":"2010-07-03T20:09:50Z","abstract_excerpt":"We construct motivic invariants of a subvariety of an algebraic torus from its tropicalization and initial degenerations. More specifically, we introduce an invariant of a compactification of such a variety called the \"tropical motivic nearby fiber.\" This invariant specializes in the schon case to the Hodge-Deligne polynomial of the limit mixed Hodge structure of a corresponding degeneration. We give purely combinatorial expressions for this Hodge-Deligne polynomial in the cases of schon hypersurfaces and smooth tropical varieties. We also deduce a formula for the Euler characteristic of a gen"},"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":"1007.0511","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-07-03T20:09:50Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"edd8991d71d1cb736669a15b8e901f83d7227e4e73843cd6af9f2226d1cf7056","abstract_canon_sha256":"22faa97ea7df3f22d3b2890c1dc6ae658ea7963bc4c85df9be895ec24eb30d23"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:19.702043Z","signature_b64":"3CYJX0Q2xIyYs/g6j8zqR88DgMD7djNawk+TS9SvTvD7wXa7aHn7uvF/LmzHFQPuXz9KfIIzvbZly5L0XrpNCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfda651f5da4b2624b335c82ce0c53f6bd817add3328182745b9a90bac1361a7","last_reissued_at":"2026-05-17T23:53:19.701451Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:19.701451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tropical Geometry and the Motivic Nearby Fiber","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Alan Stapledon, Eric Katz","submitted_at":"2010-07-03T20:09:50Z","abstract_excerpt":"We construct motivic invariants of a subvariety of an algebraic torus from its tropicalization and initial degenerations. More specifically, we introduce an invariant of a compactification of such a variety called the \"tropical motivic nearby fiber.\" This invariant specializes in the schon case to the Hodge-Deligne polynomial of the limit mixed Hodge structure of a corresponding degeneration. We give purely combinatorial expressions for this Hodge-Deligne polynomial in the cases of schon hypersurfaces and smooth tropical varieties. We also deduce a formula for the Euler characteristic of a gen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0511","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":"1007.0511","created_at":"2026-05-17T23:53:19.701532+00:00"},{"alias_kind":"arxiv_version","alias_value":"1007.0511v2","created_at":"2026-05-17T23:53:19.701532+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0511","created_at":"2026-05-17T23:53:19.701532+00:00"},{"alias_kind":"pith_short_12","alias_value":"X7NGKH25USZG","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"X7NGKH25USZGESZT","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"X7NGKH25","created_at":"2026-05-18T12:26:17.028572+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/X7NGKH25USZGESZTLSBM4DCT62","json":"https://pith.science/pith/X7NGKH25USZGESZTLSBM4DCT62.json","graph_json":"https://pith.science/api/pith-number/X7NGKH25USZGESZTLSBM4DCT62/graph.json","events_json":"https://pith.science/api/pith-number/X7NGKH25USZGESZTLSBM4DCT62/events.json","paper":"https://pith.science/paper/X7NGKH25"},"agent_actions":{"view_html":"https://pith.science/pith/X7NGKH25USZGESZTLSBM4DCT62","download_json":"https://pith.science/pith/X7NGKH25USZGESZTLSBM4DCT62.json","view_paper":"https://pith.science/paper/X7NGKH25","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1007.0511&json=true","fetch_graph":"https://pith.science/api/pith-number/X7NGKH25USZGESZTLSBM4DCT62/graph.json","fetch_events":"https://pith.science/api/pith-number/X7NGKH25USZGESZTLSBM4DCT62/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X7NGKH25USZGESZTLSBM4DCT62/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X7NGKH25USZGESZTLSBM4DCT62/action/storage_attestation","attest_author":"https://pith.science/pith/X7NGKH25USZGESZTLSBM4DCT62/action/author_attestation","sign_citation":"https://pith.science/pith/X7NGKH25USZGESZTLSBM4DCT62/action/citation_signature","submit_replication":"https://pith.science/pith/X7NGKH25USZGESZTLSBM4DCT62/action/replication_record"}},"created_at":"2026-05-17T23:53:19.701532+00:00","updated_at":"2026-05-17T23:53:19.701532+00:00"}