{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:X36GR2NBTV35RIVDCK5OVYR6XM","short_pith_number":"pith:X36GR2NB","canonical_record":{"source":{"id":"2501.04245","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-01-08T03:09:51Z","cross_cats_sorted":[],"title_canon_sha256":"c2d1b9ebd4a4f81e970f72a22497c4cf4b3b2a66ae8554b61f96f878294be34f","abstract_canon_sha256":"05e89bcb2904f0b62219f29fee2455e2f8566f4fda83582e31b58bf862547bc7"},"schema_version":"1.0"},"canonical_sha256":"befc68e9a19d77d8a2a312baeae23ebb26e9377a4876ae10c520898c1dbfa357","source":{"kind":"arxiv","id":"2501.04245","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.04245","created_at":"2026-07-05T09:58:32Z"},{"alias_kind":"arxiv_version","alias_value":"2501.04245v1","created_at":"2026-07-05T09:58:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.04245","created_at":"2026-07-05T09:58:32Z"},{"alias_kind":"pith_short_12","alias_value":"X36GR2NBTV35","created_at":"2026-07-05T09:58:32Z"},{"alias_kind":"pith_short_16","alias_value":"X36GR2NBTV35RIVD","created_at":"2026-07-05T09:58:32Z"},{"alias_kind":"pith_short_8","alias_value":"X36GR2NB","created_at":"2026-07-05T09:58:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:X36GR2NBTV35RIVDCK5OVYR6XM","target":"record","payload":{"canonical_record":{"source":{"id":"2501.04245","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-01-08T03:09:51Z","cross_cats_sorted":[],"title_canon_sha256":"c2d1b9ebd4a4f81e970f72a22497c4cf4b3b2a66ae8554b61f96f878294be34f","abstract_canon_sha256":"05e89bcb2904f0b62219f29fee2455e2f8566f4fda83582e31b58bf862547bc7"},"schema_version":"1.0"},"canonical_sha256":"befc68e9a19d77d8a2a312baeae23ebb26e9377a4876ae10c520898c1dbfa357","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:58:32.167798Z","signature_b64":"e4HthpH8ocJMQ8Q4n/yhRjRx/v1tx0yA0RtMqdQJaZ/PSz8c0Epta4QAo1kj19iA0Ea3Dr5oSyW4maJFGmpICA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"befc68e9a19d77d8a2a312baeae23ebb26e9377a4876ae10c520898c1dbfa357","last_reissued_at":"2026-07-05T09:58:32.167341Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:58:32.167341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.04245","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":"2026-07-05T09:58:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PY5pvcD+D2R2yJ6jrj20f6T5z/vNzcoLRcwpemG+KsKYoIRH0rjukJE5bKgU/SAmINqewgK/bHhMWQ20tm7gDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T10:45:07.283710Z"},"content_sha256":"10c229f1c93c9a77d65e0a9ca9db6c43613df49b4621231cab944a96d4199d7f","schema_version":"1.0","event_id":"sha256:10c229f1c93c9a77d65e0a9ca9db6c43613df49b4621231cab944a96d4199d7f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:X36GR2NBTV35RIVDCK5OVYR6XM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A symmetric function approach to log-concavity of independence polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arthur L.B. Yang, Ethan Y.H. Li, Grace M.X. Li, Zhong-Xue Zhang","submitted_at":"2025-01-08T03:09:51Z","abstract_excerpt":"As introduced by Gutman and Harary, the independence polynomial of a graph serves as the generating polynomial of its independent sets. In 1987, Alavi, Malde, Schwenk and Erd\\H{o}s conjectured that the independence polynomials of all trees are unimodal. In this paper we come up with a new way for proving log-concavity of independence polynomials of graphs by means of their chromatic symmetric functions, which is inspired by a result of Stanley connecting properties of polynomials to positivity of symmetric functions. This method turns out to be more suitable for treating trees with irregular s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.04245","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.04245/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:58:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZcMzffimMCDbne71dSMyA8s5oLB/Sl1b1ggcnzTEy7hmwNPgevrA+d6G43NXfYIxZkm7u4h3edp6DmxsrUo5Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T10:45:07.284155Z"},"content_sha256":"7f45ed66a1b5223fe6a280e82678a2a4caf158816da41ebfac8e6d2e07f840d3","schema_version":"1.0","event_id":"sha256:7f45ed66a1b5223fe6a280e82678a2a4caf158816da41ebfac8e6d2e07f840d3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X36GR2NBTV35RIVDCK5OVYR6XM/bundle.json","state_url":"https://pith.science/pith/X36GR2NBTV35RIVDCK5OVYR6XM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X36GR2NBTV35RIVDCK5OVYR6XM/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":"2026-07-12T10:45:07Z","links":{"resolver":"https://pith.science/pith/X36GR2NBTV35RIVDCK5OVYR6XM","bundle":"https://pith.science/pith/X36GR2NBTV35RIVDCK5OVYR6XM/bundle.json","state":"https://pith.science/pith/X36GR2NBTV35RIVDCK5OVYR6XM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X36GR2NBTV35RIVDCK5OVYR6XM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:X36GR2NBTV35RIVDCK5OVYR6XM","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":"05e89bcb2904f0b62219f29fee2455e2f8566f4fda83582e31b58bf862547bc7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-01-08T03:09:51Z","title_canon_sha256":"c2d1b9ebd4a4f81e970f72a22497c4cf4b3b2a66ae8554b61f96f878294be34f"},"schema_version":"1.0","source":{"id":"2501.04245","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.04245","created_at":"2026-07-05T09:58:32Z"},{"alias_kind":"arxiv_version","alias_value":"2501.04245v1","created_at":"2026-07-05T09:58:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.04245","created_at":"2026-07-05T09:58:32Z"},{"alias_kind":"pith_short_12","alias_value":"X36GR2NBTV35","created_at":"2026-07-05T09:58:32Z"},{"alias_kind":"pith_short_16","alias_value":"X36GR2NBTV35RIVD","created_at":"2026-07-05T09:58:32Z"},{"alias_kind":"pith_short_8","alias_value":"X36GR2NB","created_at":"2026-07-05T09:58:32Z"}],"graph_snapshots":[{"event_id":"sha256:7f45ed66a1b5223fe6a280e82678a2a4caf158816da41ebfac8e6d2e07f840d3","target":"graph","created_at":"2026-07-05T09:58:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.04245/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"As introduced by Gutman and Harary, the independence polynomial of a graph serves as the generating polynomial of its independent sets. In 1987, Alavi, Malde, Schwenk and Erd\\H{o}s conjectured that the independence polynomials of all trees are unimodal. In this paper we come up with a new way for proving log-concavity of independence polynomials of graphs by means of their chromatic symmetric functions, which is inspired by a result of Stanley connecting properties of polynomials to positivity of symmetric functions. This method turns out to be more suitable for treating trees with irregular s","authors_text":"Arthur L.B. Yang, Ethan Y.H. Li, Grace M.X. Li, Zhong-Xue Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-01-08T03:09:51Z","title":"A symmetric function approach to log-concavity of independence polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.04245","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":"sha256:10c229f1c93c9a77d65e0a9ca9db6c43613df49b4621231cab944a96d4199d7f","target":"record","created_at":"2026-07-05T09:58:32Z","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":"05e89bcb2904f0b62219f29fee2455e2f8566f4fda83582e31b58bf862547bc7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-01-08T03:09:51Z","title_canon_sha256":"c2d1b9ebd4a4f81e970f72a22497c4cf4b3b2a66ae8554b61f96f878294be34f"},"schema_version":"1.0","source":{"id":"2501.04245","kind":"arxiv","version":1}},"canonical_sha256":"befc68e9a19d77d8a2a312baeae23ebb26e9377a4876ae10c520898c1dbfa357","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"befc68e9a19d77d8a2a312baeae23ebb26e9377a4876ae10c520898c1dbfa357","first_computed_at":"2026-07-05T09:58:32.167341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:58:32.167341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e4HthpH8ocJMQ8Q4n/yhRjRx/v1tx0yA0RtMqdQJaZ/PSz8c0Epta4QAo1kj19iA0Ea3Dr5oSyW4maJFGmpICA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:58:32.167798Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.04245","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10c229f1c93c9a77d65e0a9ca9db6c43613df49b4621231cab944a96d4199d7f","sha256:7f45ed66a1b5223fe6a280e82678a2a4caf158816da41ebfac8e6d2e07f840d3"],"state_sha256":"6f0e5e2626e67f6268e8353bc842888699a4199be67cab5286abb9eab50caf60"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0wjL0cmD72AbSFPDYMyWecN/Q1H2uH73JVu6nOHrlVz9hYF2glZVLTvyGbsKr0m/UnTSo/dwB0kJP/D4MaR3BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-12T10:45:07.286783Z","bundle_sha256":"578678ed3610d1cac91e24abdd83bb07de5107b838be6117a292aa8b39e78d24"}}