{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:5M3HRWZPNJV7WHQHLNMSMQEV2O","short_pith_number":"pith:5M3HRWZP","canonical_record":{"source":{"id":"1408.6176","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-26T16:13:02Z","cross_cats_sorted":[],"title_canon_sha256":"24a39614ea92f8862bd28e6307475021c1869d25a16ad7c4685ec332f69f872e","abstract_canon_sha256":"2541f624b91a724bfd1dc53c4741a2ca70e877f76d344fffa8e458f330aab80d"},"schema_version":"1.0"},"canonical_sha256":"eb3678db2f6a6bfb1e075b59264095d3a6f3f83a9e19d8df29c2baff8db0ad33","source":{"kind":"arxiv","id":"1408.6176","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6176","created_at":"2026-05-18T01:23:50Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6176v2","created_at":"2026-05-18T01:23:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6176","created_at":"2026-05-18T01:23:50Z"},{"alias_kind":"pith_short_12","alias_value":"5M3HRWZPNJV7","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5M3HRWZPNJV7WHQH","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5M3HRWZP","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:5M3HRWZPNJV7WHQHLNMSMQEV2O","target":"record","payload":{"canonical_record":{"source":{"id":"1408.6176","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-26T16:13:02Z","cross_cats_sorted":[],"title_canon_sha256":"24a39614ea92f8862bd28e6307475021c1869d25a16ad7c4685ec332f69f872e","abstract_canon_sha256":"2541f624b91a724bfd1dc53c4741a2ca70e877f76d344fffa8e458f330aab80d"},"schema_version":"1.0"},"canonical_sha256":"eb3678db2f6a6bfb1e075b59264095d3a6f3f83a9e19d8df29c2baff8db0ad33","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:50.897268Z","signature_b64":"YDsHCC3MXTnOekazR8am7h3BV2raVOKoeaQxuT5+SpflS6rQM7hlKQ+tWGdGiiliqHT4aOZG9vd829RbEiA0Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb3678db2f6a6bfb1e075b59264095d3a6f3f83a9e19d8df29c2baff8db0ad33","last_reissued_at":"2026-05-18T01:23:50.896578Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:50.896578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.6176","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":"2026-05-18T01:23:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1qyRmMhjrdFHjU3/W9vEIMqyOS9hSck0+DCdbbr6fvpFdoKlfSxM6niXH0B7QzIQguh/NhLsA0kPsvgiOoQPCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:21:23.502873Z"},"content_sha256":"a8c216eb158aa2a1b647ab748fde2c26bbb20cab57ac923a855939f4d9e4b458","schema_version":"1.0","event_id":"sha256:a8c216eb158aa2a1b647ab748fde2c26bbb20cab57ac923a855939f4d9e4b458"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:5M3HRWZPNJV7WHQHLNMSMQEV2O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tropicalization of facets of polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ricardo D. Katz, Xavier Allamigeon","submitted_at":"2014-08-26T16:13:02Z","abstract_excerpt":"It is known that any tropical polytope is the image under the valuation map of ordinary polytopes over the Puiseux series field. The latter polytopes are called lifts of the tropical polytope. We prove that any pure tropical polytope is the intersection of the tropical half-spaces given by the images under the valuation map of the facet-defining half-spaces of a certain lift. We construct this lift explicitly, taking into account geometric properties of the given polytope. Moreover, when the generators of the tropical polytope are in general position, we prove that the above property is satisf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6176","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":"2026-05-18T01:23:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fWcRn88bfG5DP0gIZAAvQpbU1jAFflK1exZwhjJ7Uvv5jiGCAnm3hFacOEz/SWyXEd2mmgrwpWtVduexMfDBCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:21:23.503598Z"},"content_sha256":"5c3aaa900ca6fb8d4b31b65d355374ea3846dcfb7f7cc747b9669c4efa865210","schema_version":"1.0","event_id":"sha256:5c3aaa900ca6fb8d4b31b65d355374ea3846dcfb7f7cc747b9669c4efa865210"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5M3HRWZPNJV7WHQHLNMSMQEV2O/bundle.json","state_url":"https://pith.science/pith/5M3HRWZPNJV7WHQHLNMSMQEV2O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5M3HRWZPNJV7WHQHLNMSMQEV2O/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":"2026-05-25T23:21:23Z","links":{"resolver":"https://pith.science/pith/5M3HRWZPNJV7WHQHLNMSMQEV2O","bundle":"https://pith.science/pith/5M3HRWZPNJV7WHQHLNMSMQEV2O/bundle.json","state":"https://pith.science/pith/5M3HRWZPNJV7WHQHLNMSMQEV2O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5M3HRWZPNJV7WHQHLNMSMQEV2O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5M3HRWZPNJV7WHQHLNMSMQEV2O","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":"2541f624b91a724bfd1dc53c4741a2ca70e877f76d344fffa8e458f330aab80d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-26T16:13:02Z","title_canon_sha256":"24a39614ea92f8862bd28e6307475021c1869d25a16ad7c4685ec332f69f872e"},"schema_version":"1.0","source":{"id":"1408.6176","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6176","created_at":"2026-05-18T01:23:50Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6176v2","created_at":"2026-05-18T01:23:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6176","created_at":"2026-05-18T01:23:50Z"},{"alias_kind":"pith_short_12","alias_value":"5M3HRWZPNJV7","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5M3HRWZPNJV7WHQH","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5M3HRWZP","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:5c3aaa900ca6fb8d4b31b65d355374ea3846dcfb7f7cc747b9669c4efa865210","target":"graph","created_at":"2026-05-18T01:23:50Z","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":"It is known that any tropical polytope is the image under the valuation map of ordinary polytopes over the Puiseux series field. The latter polytopes are called lifts of the tropical polytope. We prove that any pure tropical polytope is the intersection of the tropical half-spaces given by the images under the valuation map of the facet-defining half-spaces of a certain lift. We construct this lift explicitly, taking into account geometric properties of the given polytope. Moreover, when the generators of the tropical polytope are in general position, we prove that the above property is satisf","authors_text":"Ricardo D. Katz, Xavier Allamigeon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-26T16:13:02Z","title":"Tropicalization of facets of polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6176","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:a8c216eb158aa2a1b647ab748fde2c26bbb20cab57ac923a855939f4d9e4b458","target":"record","created_at":"2026-05-18T01:23:50Z","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":"2541f624b91a724bfd1dc53c4741a2ca70e877f76d344fffa8e458f330aab80d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-26T16:13:02Z","title_canon_sha256":"24a39614ea92f8862bd28e6307475021c1869d25a16ad7c4685ec332f69f872e"},"schema_version":"1.0","source":{"id":"1408.6176","kind":"arxiv","version":2}},"canonical_sha256":"eb3678db2f6a6bfb1e075b59264095d3a6f3f83a9e19d8df29c2baff8db0ad33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb3678db2f6a6bfb1e075b59264095d3a6f3f83a9e19d8df29c2baff8db0ad33","first_computed_at":"2026-05-18T01:23:50.896578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:50.896578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YDsHCC3MXTnOekazR8am7h3BV2raVOKoeaQxuT5+SpflS6rQM7hlKQ+tWGdGiiliqHT4aOZG9vd829RbEiA0Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:50.897268Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.6176","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8c216eb158aa2a1b647ab748fde2c26bbb20cab57ac923a855939f4d9e4b458","sha256:5c3aaa900ca6fb8d4b31b65d355374ea3846dcfb7f7cc747b9669c4efa865210"],"state_sha256":"752b1090ee44b5bb684b21528b8953a215e323cbcd775af82d1d519f9904316e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8HHcoDojTHfMiA+w2uyWvxCZDBSVf37nZ5rD5x8OWLajWKN3dmqBm13fQEWe8+Kjz1l+rW7CDG483D81YM5mBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T23:21:23.507294Z","bundle_sha256":"fa9da8dedda4f9792b9e105f9396d04e41e1e524f65f4697538dae25e7c584c0"}}