{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:SN2P735MABV665WAL3R5JBCHLW","short_pith_number":"pith:SN2P735M","canonical_record":{"source":{"id":"1104.1885","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-11T09:12:30Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"0716f0f8a9c929d815927fbe8beca8e25f14cba0da7bbb6bfc79f0a322e869c2","abstract_canon_sha256":"02776312156148575ff4e4d5c4a72d5f52443c4ecd667c6031efb46d0cd7b3dc"},"schema_version":"1.0"},"canonical_sha256":"9374ffefac006bef76c05ee3d484475d9a913ee17f09580fd68e3344bef0f476","source":{"kind":"arxiv","id":"1104.1885","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1885","created_at":"2026-05-18T02:22:10Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1885v1","created_at":"2026-05-18T02:22:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1885","created_at":"2026-05-18T02:22:10Z"},{"alias_kind":"pith_short_12","alias_value":"SN2P735MABV6","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SN2P735MABV665WA","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SN2P735M","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:SN2P735MABV665WAL3R5JBCHLW","target":"record","payload":{"canonical_record":{"source":{"id":"1104.1885","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-11T09:12:30Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"0716f0f8a9c929d815927fbe8beca8e25f14cba0da7bbb6bfc79f0a322e869c2","abstract_canon_sha256":"02776312156148575ff4e4d5c4a72d5f52443c4ecd667c6031efb46d0cd7b3dc"},"schema_version":"1.0"},"canonical_sha256":"9374ffefac006bef76c05ee3d484475d9a913ee17f09580fd68e3344bef0f476","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:10.080768Z","signature_b64":"YxkzlIWM8Y5+dZpVa3s4jzC5Sx6+89qZcpHwi6Snr5/VIGqqdWSNoOm5J2fRQHb6tj99xtaIxfXT3F3Tq2d/Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9374ffefac006bef76c05ee3d484475d9a913ee17f09580fd68e3344bef0f476","last_reissued_at":"2026-05-18T02:22:10.080227Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:10.080227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.1885","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":"2026-05-18T02:22:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WHPh6WTZixDdseasfQ9GHMbRotjFhh1EixS/4jNFgjXzYRZEuA798xyGess2wGhZZ1Sk4X6xAyui3fikSGdODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:24:48.367881Z"},"content_sha256":"23297a33282b017a9a3fe064be7d1f97f157ed2b6d1f9870a8fbba072199c443","schema_version":"1.0","event_id":"sha256:23297a33282b017a9a3fe064be7d1f97f157ed2b6d1f9870a8fbba072199c443"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:SN2P735MABV665WAL3R5JBCHLW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytic continuation of a parametric polytope and wall-crossing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Mich\\`ele Vergne, Nicole Berline","submitted_at":"2011-04-11T09:12:30Z","abstract_excerpt":"We define a set theoretic \"analytic continuation\" of a polytope defined by inequalities. For the regular values of the parameter, our construction coincides with the parallel transport of polytopes in a mirage introduced by Varchenko. We determine the set-theoretic variation when crossing a wall in the parameter space, and we relate this variation to Paradan's wall-crossing formulas for integrals and discrete sums. As another application, we refine the theorem of Brion on generating functions of polytopes and their cones at vertices. We describe the relation of this work with the equivariant i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1885","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":""},"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":"2026-05-18T02:22:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"whis94Ri+5kgypwioxx9O1nEqBss7HHFiqc0jAt237Yqyn9Teeuch2lCVgo4wSglsBZtFps5MWVfaKIvljItDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:24:48.368226Z"},"content_sha256":"060466c17eb64db1bf69c313cfcf282c080a9e9d82ac131935a4248c4a582693","schema_version":"1.0","event_id":"sha256:060466c17eb64db1bf69c313cfcf282c080a9e9d82ac131935a4248c4a582693"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SN2P735MABV665WAL3R5JBCHLW/bundle.json","state_url":"https://pith.science/pith/SN2P735MABV665WAL3R5JBCHLW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SN2P735MABV665WAL3R5JBCHLW/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":"2026-06-23T21:24:48Z","links":{"resolver":"https://pith.science/pith/SN2P735MABV665WAL3R5JBCHLW","bundle":"https://pith.science/pith/SN2P735MABV665WAL3R5JBCHLW/bundle.json","state":"https://pith.science/pith/SN2P735MABV665WAL3R5JBCHLW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SN2P735MABV665WAL3R5JBCHLW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SN2P735MABV665WAL3R5JBCHLW","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":"02776312156148575ff4e4d5c4a72d5f52443c4ecd667c6031efb46d0cd7b3dc","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-11T09:12:30Z","title_canon_sha256":"0716f0f8a9c929d815927fbe8beca8e25f14cba0da7bbb6bfc79f0a322e869c2"},"schema_version":"1.0","source":{"id":"1104.1885","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1885","created_at":"2026-05-18T02:22:10Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1885v1","created_at":"2026-05-18T02:22:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1885","created_at":"2026-05-18T02:22:10Z"},{"alias_kind":"pith_short_12","alias_value":"SN2P735MABV6","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SN2P735MABV665WA","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SN2P735M","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:060466c17eb64db1bf69c313cfcf282c080a9e9d82ac131935a4248c4a582693","target":"graph","created_at":"2026-05-18T02:22:10Z","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 define a set theoretic \"analytic continuation\" of a polytope defined by inequalities. For the regular values of the parameter, our construction coincides with the parallel transport of polytopes in a mirage introduced by Varchenko. We determine the set-theoretic variation when crossing a wall in the parameter space, and we relate this variation to Paradan's wall-crossing formulas for integrals and discrete sums. As another application, we refine the theorem of Brion on generating functions of polytopes and their cones at vertices. We describe the relation of this work with the equivariant i","authors_text":"Mich\\`ele Vergne, Nicole Berline","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-11T09:12:30Z","title":"Analytic continuation of a parametric polytope and wall-crossing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1885","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":"sha256:23297a33282b017a9a3fe064be7d1f97f157ed2b6d1f9870a8fbba072199c443","target":"record","created_at":"2026-05-18T02:22:10Z","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":"02776312156148575ff4e4d5c4a72d5f52443c4ecd667c6031efb46d0cd7b3dc","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-11T09:12:30Z","title_canon_sha256":"0716f0f8a9c929d815927fbe8beca8e25f14cba0da7bbb6bfc79f0a322e869c2"},"schema_version":"1.0","source":{"id":"1104.1885","kind":"arxiv","version":1}},"canonical_sha256":"9374ffefac006bef76c05ee3d484475d9a913ee17f09580fd68e3344bef0f476","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9374ffefac006bef76c05ee3d484475d9a913ee17f09580fd68e3344bef0f476","first_computed_at":"2026-05-18T02:22:10.080227Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:10.080227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YxkzlIWM8Y5+dZpVa3s4jzC5Sx6+89qZcpHwi6Snr5/VIGqqdWSNoOm5J2fRQHb6tj99xtaIxfXT3F3Tq2d/Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:10.080768Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.1885","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23297a33282b017a9a3fe064be7d1f97f157ed2b6d1f9870a8fbba072199c443","sha256:060466c17eb64db1bf69c313cfcf282c080a9e9d82ac131935a4248c4a582693"],"state_sha256":"d9aa061145b3e70c4ebdf05b7d0cd1bbdc5257d1d0faf5fe15fd4f4b42e19d32"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MHT3U0pVr35DpRAqlLVewI1lxowpmtGQ18IW3ZCw8dspmqgQ/rYJkH2Ghc8fpYe3N2Gviu7gx1iSWPm29k8LCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T21:24:48.370274Z","bundle_sha256":"74f55059f77a3ade0c4b19dc24c6b623ac4d671df4b51b4a24fc8b7cdcb0176b"}}