{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:CE7TFOJ4LLIUVMBHMX2TJPHRTC","short_pith_number":"pith:CE7TFOJ4","canonical_record":{"source":{"id":"1501.06105","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-25T02:02:31Z","cross_cats_sorted":[],"title_canon_sha256":"ec54a153460d7d0e1a971d5ed03ab99b273ba8a51f385ea7c07086666f2e4fb7","abstract_canon_sha256":"92d2e32aa7d5706b14909fd462984098d81b2dc16c1f7441fcb5a6617f9c9f6e"},"schema_version":"1.0"},"canonical_sha256":"113f32b93c5ad14ab02765f534bcf198984d9c8e7c2aa3298461a66796055b66","source":{"kind":"arxiv","id":"1501.06105","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06105","created_at":"2026-05-18T02:28:42Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06105v1","created_at":"2026-05-18T02:28:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06105","created_at":"2026-05-18T02:28:42Z"},{"alias_kind":"pith_short_12","alias_value":"CE7TFOJ4LLIU","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"CE7TFOJ4LLIUVMBH","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"CE7TFOJ4","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:CE7TFOJ4LLIUVMBHMX2TJPHRTC","target":"record","payload":{"canonical_record":{"source":{"id":"1501.06105","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-25T02:02:31Z","cross_cats_sorted":[],"title_canon_sha256":"ec54a153460d7d0e1a971d5ed03ab99b273ba8a51f385ea7c07086666f2e4fb7","abstract_canon_sha256":"92d2e32aa7d5706b14909fd462984098d81b2dc16c1f7441fcb5a6617f9c9f6e"},"schema_version":"1.0"},"canonical_sha256":"113f32b93c5ad14ab02765f534bcf198984d9c8e7c2aa3298461a66796055b66","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:42.342806Z","signature_b64":"QW5hOGSRnnueMrL9BasqezuB01tynambJZcx5XcM/LPLboHRtJ4lL5cHheF2bpBBuAzcT2b3M2+lMdCYnYnEBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"113f32b93c5ad14ab02765f534bcf198984d9c8e7c2aa3298461a66796055b66","last_reissued_at":"2026-05-18T02:28:42.342351Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:42.342351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.06105","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":"2026-05-18T02:28:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"90t7BuIPT1jLKDtxxp+RrrfvvHZtlzmOBb+ytFi68qY/I8tB6ehvjv8xBFAe4FfnatIvH/6ex9nBGeQro32QDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:09:35.140058Z"},"content_sha256":"07ff58ed8a8fe41b928cc0bef5da5921b09357610c822cb9ce42e235ee23276e","schema_version":"1.0","event_id":"sha256:07ff58ed8a8fe41b928cc0bef5da5921b09357610c822cb9ce42e235ee23276e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:CE7TFOJ4LLIUVMBHMX2TJPHRTC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Iterated claws have real-rooted genus polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"D.G.L. Wang, J.L. Gross, T. Mansour, T.W. Tucker","submitted_at":"2015-01-25T02:02:31Z","abstract_excerpt":"We prove that the genus polynomials of the graphs called iterated claws are real-rooted. This continues our work directed toward the 25-year-old conjecture that the genus distribution of every graph is log-concave. We have previously established log-concavity for sequences of graphs constructed by iterative vertex-amalgamation or iterative edge-amalgamation of graphs that satisfy a commonly observable condition on their partitioned genus distributions, even though it had been proved previously that iterative amalgamation does not always preserve real-rootedness of the genus polynomial of the i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06105","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":"2026-05-18T02:28:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kqHoQ6rKj8lDy1Kj/yyKpUN4Xf8KwyjB5is20ybHKny9I51FHljyD3DpUtOszJrgFmnfGwHdRfmYNHhnOvq4Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:09:35.140723Z"},"content_sha256":"3530b3698bba7e9c75986ccfddeba147d97329f2230ccdd81b50df2f9cbc348c","schema_version":"1.0","event_id":"sha256:3530b3698bba7e9c75986ccfddeba147d97329f2230ccdd81b50df2f9cbc348c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CE7TFOJ4LLIUVMBHMX2TJPHRTC/bundle.json","state_url":"https://pith.science/pith/CE7TFOJ4LLIUVMBHMX2TJPHRTC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CE7TFOJ4LLIUVMBHMX2TJPHRTC/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":"2026-06-05T21:09:35Z","links":{"resolver":"https://pith.science/pith/CE7TFOJ4LLIUVMBHMX2TJPHRTC","bundle":"https://pith.science/pith/CE7TFOJ4LLIUVMBHMX2TJPHRTC/bundle.json","state":"https://pith.science/pith/CE7TFOJ4LLIUVMBHMX2TJPHRTC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CE7TFOJ4LLIUVMBHMX2TJPHRTC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CE7TFOJ4LLIUVMBHMX2TJPHRTC","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":"92d2e32aa7d5706b14909fd462984098d81b2dc16c1f7441fcb5a6617f9c9f6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-25T02:02:31Z","title_canon_sha256":"ec54a153460d7d0e1a971d5ed03ab99b273ba8a51f385ea7c07086666f2e4fb7"},"schema_version":"1.0","source":{"id":"1501.06105","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06105","created_at":"2026-05-18T02:28:42Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06105v1","created_at":"2026-05-18T02:28:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06105","created_at":"2026-05-18T02:28:42Z"},{"alias_kind":"pith_short_12","alias_value":"CE7TFOJ4LLIU","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"CE7TFOJ4LLIUVMBH","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"CE7TFOJ4","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:3530b3698bba7e9c75986ccfddeba147d97329f2230ccdd81b50df2f9cbc348c","target":"graph","created_at":"2026-05-18T02:28:42Z","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 prove that the genus polynomials of the graphs called iterated claws are real-rooted. This continues our work directed toward the 25-year-old conjecture that the genus distribution of every graph is log-concave. We have previously established log-concavity for sequences of graphs constructed by iterative vertex-amalgamation or iterative edge-amalgamation of graphs that satisfy a commonly observable condition on their partitioned genus distributions, even though it had been proved previously that iterative amalgamation does not always preserve real-rootedness of the genus polynomial of the i","authors_text":"D.G.L. Wang, J.L. Gross, T. Mansour, T.W. Tucker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-25T02:02:31Z","title":"Iterated claws have real-rooted genus polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06105","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":"sha256:07ff58ed8a8fe41b928cc0bef5da5921b09357610c822cb9ce42e235ee23276e","target":"record","created_at":"2026-05-18T02:28:42Z","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":"92d2e32aa7d5706b14909fd462984098d81b2dc16c1f7441fcb5a6617f9c9f6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-25T02:02:31Z","title_canon_sha256":"ec54a153460d7d0e1a971d5ed03ab99b273ba8a51f385ea7c07086666f2e4fb7"},"schema_version":"1.0","source":{"id":"1501.06105","kind":"arxiv","version":1}},"canonical_sha256":"113f32b93c5ad14ab02765f534bcf198984d9c8e7c2aa3298461a66796055b66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"113f32b93c5ad14ab02765f534bcf198984d9c8e7c2aa3298461a66796055b66","first_computed_at":"2026-05-18T02:28:42.342351Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:42.342351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QW5hOGSRnnueMrL9BasqezuB01tynambJZcx5XcM/LPLboHRtJ4lL5cHheF2bpBBuAzcT2b3M2+lMdCYnYnEBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:42.342806Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.06105","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07ff58ed8a8fe41b928cc0bef5da5921b09357610c822cb9ce42e235ee23276e","sha256:3530b3698bba7e9c75986ccfddeba147d97329f2230ccdd81b50df2f9cbc348c"],"state_sha256":"de1a460201a6bf88c3021d99dadacc197b4ac05c7eba1d2eca7cb09abb33e19f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y1K4aedAlqt6DzodGJGZtDyWJYZL8zIaV1/R5Bawr4c8cPeOck30ClyU1a33+i8cfgNgDePOknRWZT11SKT7Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T21:09:35.145553Z","bundle_sha256":"aada1df3383cefc5672915575cb985803060f9dd8cec454d1a10e4885230458e"}}