{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LNFUHJYQVIWIQ64POAARAZ4MX3","short_pith_number":"pith:LNFUHJYQ","canonical_record":{"source":{"id":"1605.05287","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-17T19:00:26Z","cross_cats_sorted":[],"title_canon_sha256":"4ef07f0451c6d27becdee594ac42092a78de63cfad800455707aa4564840fe8c","abstract_canon_sha256":"6720f8ca422f0968760c0fbe6a4f2d93778e5b1e164b11cd48f24fc44967a01e"},"schema_version":"1.0"},"canonical_sha256":"5b4b43a710aa2c887b8f700110678cbecb16c944af4fe5f2f0f6a8537957650e","source":{"kind":"arxiv","id":"1605.05287","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.05287","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"1605.05287v1","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05287","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"LNFUHJYQVIWI","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LNFUHJYQVIWIQ64P","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LNFUHJYQ","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LNFUHJYQVIWIQ64POAARAZ4MX3","target":"record","payload":{"canonical_record":{"source":{"id":"1605.05287","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-17T19:00:26Z","cross_cats_sorted":[],"title_canon_sha256":"4ef07f0451c6d27becdee594ac42092a78de63cfad800455707aa4564840fe8c","abstract_canon_sha256":"6720f8ca422f0968760c0fbe6a4f2d93778e5b1e164b11cd48f24fc44967a01e"},"schema_version":"1.0"},"canonical_sha256":"5b4b43a710aa2c887b8f700110678cbecb16c944af4fe5f2f0f6a8537957650e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:36.782424Z","signature_b64":"euhyJyHL5AnTEWJNDuXbgPQ7HaExRPg0vWFOhPiePewumYvHJAB98fsRjVWwXZSRRehLOmap4vMnSYidKahTBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b4b43a710aa2c887b8f700110678cbecb16c944af4fe5f2f0f6a8537957650e","last_reissued_at":"2026-05-18T01:14:36.781707Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:36.781707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.05287","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":"2026-05-18T01:14:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Btq55t0e7/fbdY9U2kcTxKmQNRqsFFZi+nWMshniW50ueakUuF41XZP5WRiGi2pq9kw9ErOG4CJ6DfOXJx5FBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:57:13.418936Z"},"content_sha256":"cbcb702145098380a8158442ec427cf1b6553459e41438a1f1ad47009ce76924","schema_version":"1.0","event_id":"sha256:cbcb702145098380a8158442ec427cf1b6553459e41438a1f1ad47009ce76924"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LNFUHJYQVIWIQ64POAARAZ4MX3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compatible polynomials and edgewise subdivisions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Madeleine Leander","submitted_at":"2016-05-17T19:00:26Z","abstract_excerpt":"In this paper we answer a question posed by C. A. Athanasiadis. Namely, we prove that the local $h$-polynomial of the $r$th edgewise subdivision of the $(n-1)$-dimensional simplex $2^V$ has only real zeros. In doing so we find a tool, using compatible polynomials, that can be used to check if polynomials in certain types of families of polynomials have only real zeros."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05287","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":"2026-05-18T01:14:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dcxGJpuD7vvt5lC+3EmEbaceBaldkWX52MdemUxyt92wU9ADL0XotaDe9GTHkEPw0cjPfYHhpiJZduBXfc+CDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:57:13.419285Z"},"content_sha256":"3595175a231e4b49e233006145799a28718e40514705d854e87e5316bbf190c6","schema_version":"1.0","event_id":"sha256:3595175a231e4b49e233006145799a28718e40514705d854e87e5316bbf190c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LNFUHJYQVIWIQ64POAARAZ4MX3/bundle.json","state_url":"https://pith.science/pith/LNFUHJYQVIWIQ64POAARAZ4MX3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LNFUHJYQVIWIQ64POAARAZ4MX3/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":"2026-06-22T18:57:13Z","links":{"resolver":"https://pith.science/pith/LNFUHJYQVIWIQ64POAARAZ4MX3","bundle":"https://pith.science/pith/LNFUHJYQVIWIQ64POAARAZ4MX3/bundle.json","state":"https://pith.science/pith/LNFUHJYQVIWIQ64POAARAZ4MX3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LNFUHJYQVIWIQ64POAARAZ4MX3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LNFUHJYQVIWIQ64POAARAZ4MX3","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":"6720f8ca422f0968760c0fbe6a4f2d93778e5b1e164b11cd48f24fc44967a01e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-17T19:00:26Z","title_canon_sha256":"4ef07f0451c6d27becdee594ac42092a78de63cfad800455707aa4564840fe8c"},"schema_version":"1.0","source":{"id":"1605.05287","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.05287","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"1605.05287v1","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05287","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"LNFUHJYQVIWI","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LNFUHJYQVIWIQ64P","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LNFUHJYQ","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:3595175a231e4b49e233006145799a28718e40514705d854e87e5316bbf190c6","target":"graph","created_at":"2026-05-18T01:14:36Z","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":"In this paper we answer a question posed by C. A. Athanasiadis. Namely, we prove that the local $h$-polynomial of the $r$th edgewise subdivision of the $(n-1)$-dimensional simplex $2^V$ has only real zeros. In doing so we find a tool, using compatible polynomials, that can be used to check if polynomials in certain types of families of polynomials have only real zeros.","authors_text":"Madeleine Leander","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-17T19:00:26Z","title":"Compatible polynomials and edgewise subdivisions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05287","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:cbcb702145098380a8158442ec427cf1b6553459e41438a1f1ad47009ce76924","target":"record","created_at":"2026-05-18T01:14:36Z","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":"6720f8ca422f0968760c0fbe6a4f2d93778e5b1e164b11cd48f24fc44967a01e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-17T19:00:26Z","title_canon_sha256":"4ef07f0451c6d27becdee594ac42092a78de63cfad800455707aa4564840fe8c"},"schema_version":"1.0","source":{"id":"1605.05287","kind":"arxiv","version":1}},"canonical_sha256":"5b4b43a710aa2c887b8f700110678cbecb16c944af4fe5f2f0f6a8537957650e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b4b43a710aa2c887b8f700110678cbecb16c944af4fe5f2f0f6a8537957650e","first_computed_at":"2026-05-18T01:14:36.781707Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:36.781707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"euhyJyHL5AnTEWJNDuXbgPQ7HaExRPg0vWFOhPiePewumYvHJAB98fsRjVWwXZSRRehLOmap4vMnSYidKahTBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:36.782424Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.05287","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbcb702145098380a8158442ec427cf1b6553459e41438a1f1ad47009ce76924","sha256:3595175a231e4b49e233006145799a28718e40514705d854e87e5316bbf190c6"],"state_sha256":"c8f5590dae79ee997c82f3758f0f0b601c96a7db76a418efdfed34bbfe0f2ed3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ygdP8FEnCO3mdKercnpu6QNLFkTjW+NDVbqH2SCKth0f6jh/0Ieohs4h/KOwHQ2LfMsll99xJPkpZ7rm7gmxDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T18:57:13.421138Z","bundle_sha256":"4c925faa57658063ae4a5018b5c8affd2bf3eb79231b4a572b1e465ab6abeb43"}}