{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FU6OOORFRKXAI3Z2NDIGNB7C27","short_pith_number":"pith:FU6OOORF","canonical_record":{"source":{"id":"1807.01180","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-03T13:36:16Z","cross_cats_sorted":[],"title_canon_sha256":"7c8b4590a6d48350dca48f9f70d74a7337d37386c7eeda85f7e39fd013875c63","abstract_canon_sha256":"4bd41f7eebe75d4e631a4e36e03aa2d7aa0b7c2f8368010219395f3f2a989626"},"schema_version":"1.0"},"canonical_sha256":"2d3ce73a258aae046f3a68d06687e2d7e5f20d9bcaa1fec74e8a1962d79cf5b1","source":{"kind":"arxiv","id":"1807.01180","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.01180","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"1807.01180v1","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01180","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"FU6OOORFRKXA","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FU6OOORFRKXAI3Z2","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FU6OOORF","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FU6OOORFRKXAI3Z2NDIGNB7C27","target":"record","payload":{"canonical_record":{"source":{"id":"1807.01180","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-03T13:36:16Z","cross_cats_sorted":[],"title_canon_sha256":"7c8b4590a6d48350dca48f9f70d74a7337d37386c7eeda85f7e39fd013875c63","abstract_canon_sha256":"4bd41f7eebe75d4e631a4e36e03aa2d7aa0b7c2f8368010219395f3f2a989626"},"schema_version":"1.0"},"canonical_sha256":"2d3ce73a258aae046f3a68d06687e2d7e5f20d9bcaa1fec74e8a1962d79cf5b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:45.008974Z","signature_b64":"ZtX6FkPElsx8MDB9Hm6yz8uoLoYnyVtYBoE6Aba56sR8SlVnrvGeJfTg1aplg3XB62GfJLEkhG8ZjtvESuD0Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d3ce73a258aae046f3a68d06687e2d7e5f20d9bcaa1fec74e8a1962d79cf5b1","last_reissued_at":"2026-05-18T00:11:45.008302Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:45.008302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.01180","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":"2026-05-18T00:11:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/O4muMnU0Bzekq0vYSkB8Fz4DwUliS9q837y0ES6KMjj3M+1/IJe5Sb1dGaRg+3XfWFm3cNQlOlPLu2C9NlXBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:46:49.145030Z"},"content_sha256":"b7624e6e102795a111f80da667c5b9de49a6f64d071616d4e81fd0a4a844325a","schema_version":"1.0","event_id":"sha256:b7624e6e102795a111f80da667c5b9de49a6f64d071616d4e81fd0a4a844325a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FU6OOORFRKXAI3Z2NDIGNB7C27","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The matching polynomials and spectral radii of uniform supertrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Erfang Shan, Honghai Li, Li Su, Liying Kang","submitted_at":"2018-07-03T13:36:16Z","abstract_excerpt":"We study matching polynomials of uniform hypergraph and spectral radii of uniform supertrees. By comparing the matching polynomials of supertrees, we extend Li and Feng's results on grafting operations on graphs to supertrees. Using the methods of grafting operations on supertrees and comparing matching polynomials of supertrees, we determine the first $\\lfloor\\frac{d}{2}\\rfloor+1$ largest spectral radii of $r$-uniform supertrees with size $m$ and diameter $d$. In addition, the first two smallest spectral radii of supertrees with size $m$ are determined."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01180","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":"2026-05-18T00:11:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ir5Q+d4jWPiAKIC1v11O0AtoojCcHnSNvKZBnXxJo7p/KPxj84MR5NGj6bO24f0LC6JicoVm/3ySn9oPlq3mBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:46:49.145670Z"},"content_sha256":"931c9f518b2811fed2b9d1e255514506ae78db7be0d6005a70c735f70344dd6a","schema_version":"1.0","event_id":"sha256:931c9f518b2811fed2b9d1e255514506ae78db7be0d6005a70c735f70344dd6a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FU6OOORFRKXAI3Z2NDIGNB7C27/bundle.json","state_url":"https://pith.science/pith/FU6OOORFRKXAI3Z2NDIGNB7C27/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FU6OOORFRKXAI3Z2NDIGNB7C27/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":"2026-05-27T08:46:49Z","links":{"resolver":"https://pith.science/pith/FU6OOORFRKXAI3Z2NDIGNB7C27","bundle":"https://pith.science/pith/FU6OOORFRKXAI3Z2NDIGNB7C27/bundle.json","state":"https://pith.science/pith/FU6OOORFRKXAI3Z2NDIGNB7C27/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FU6OOORFRKXAI3Z2NDIGNB7C27/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FU6OOORFRKXAI3Z2NDIGNB7C27","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":"4bd41f7eebe75d4e631a4e36e03aa2d7aa0b7c2f8368010219395f3f2a989626","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-03T13:36:16Z","title_canon_sha256":"7c8b4590a6d48350dca48f9f70d74a7337d37386c7eeda85f7e39fd013875c63"},"schema_version":"1.0","source":{"id":"1807.01180","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.01180","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"1807.01180v1","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01180","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"FU6OOORFRKXA","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FU6OOORFRKXAI3Z2","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FU6OOORF","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:931c9f518b2811fed2b9d1e255514506ae78db7be0d6005a70c735f70344dd6a","target":"graph","created_at":"2026-05-18T00:11:45Z","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 study matching polynomials of uniform hypergraph and spectral radii of uniform supertrees. By comparing the matching polynomials of supertrees, we extend Li and Feng's results on grafting operations on graphs to supertrees. Using the methods of grafting operations on supertrees and comparing matching polynomials of supertrees, we determine the first $\\lfloor\\frac{d}{2}\\rfloor+1$ largest spectral radii of $r$-uniform supertrees with size $m$ and diameter $d$. In addition, the first two smallest spectral radii of supertrees with size $m$ are determined.","authors_text":"Erfang Shan, Honghai Li, Li Su, Liying Kang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-03T13:36:16Z","title":"The matching polynomials and spectral radii of uniform supertrees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01180","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:b7624e6e102795a111f80da667c5b9de49a6f64d071616d4e81fd0a4a844325a","target":"record","created_at":"2026-05-18T00:11:45Z","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":"4bd41f7eebe75d4e631a4e36e03aa2d7aa0b7c2f8368010219395f3f2a989626","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-03T13:36:16Z","title_canon_sha256":"7c8b4590a6d48350dca48f9f70d74a7337d37386c7eeda85f7e39fd013875c63"},"schema_version":"1.0","source":{"id":"1807.01180","kind":"arxiv","version":1}},"canonical_sha256":"2d3ce73a258aae046f3a68d06687e2d7e5f20d9bcaa1fec74e8a1962d79cf5b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d3ce73a258aae046f3a68d06687e2d7e5f20d9bcaa1fec74e8a1962d79cf5b1","first_computed_at":"2026-05-18T00:11:45.008302Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:45.008302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZtX6FkPElsx8MDB9Hm6yz8uoLoYnyVtYBoE6Aba56sR8SlVnrvGeJfTg1aplg3XB62GfJLEkhG8ZjtvESuD0Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:45.008974Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.01180","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7624e6e102795a111f80da667c5b9de49a6f64d071616d4e81fd0a4a844325a","sha256:931c9f518b2811fed2b9d1e255514506ae78db7be0d6005a70c735f70344dd6a"],"state_sha256":"bd4f56e5a984372bcf9f9768225c9a4f2c55894692dc5a359fab4b67f3342e3f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bR3AMqLqDVzu0w52YHFhShekK+loWdRt2hZBmjkrQxp6kNfqEXq0Fui+gX6fmyPPK3gTWgvIcIH0o/if7Pz7Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T08:46:49.148887Z","bundle_sha256":"0edf282532f981ede64fa2640ddd8b79eb4bfb872ed5473f061096b2d9b52ad6"}}