{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:UDGACMIPUTS3ZY65RC6HQ3ZYN5","short_pith_number":"pith:UDGACMIP","canonical_record":{"source":{"id":"2606.17356","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-15T23:11:38Z","cross_cats_sorted":[],"title_canon_sha256":"6d1c919f613a4917c5f79de6984c81801e9ab91ed166e0e64ac32bffddef08a2","abstract_canon_sha256":"97acdf485127b6f30dbab641f9e52c94b11ede899cc7aaad46982ed981502903"},"schema_version":"1.0"},"canonical_sha256":"a0cc01310fa4e5bce3dd88bc786f386f799ff03ff98f42e73253d454bc8d01c4","source":{"kind":"arxiv","id":"2606.17356","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.17356","created_at":"2026-06-19T16:10:10Z"},{"alias_kind":"arxiv_version","alias_value":"2606.17356v1","created_at":"2026-06-19T16:10:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17356","created_at":"2026-06-19T16:10:10Z"},{"alias_kind":"pith_short_12","alias_value":"UDGACMIPUTS3","created_at":"2026-06-19T16:10:10Z"},{"alias_kind":"pith_short_16","alias_value":"UDGACMIPUTS3ZY65","created_at":"2026-06-19T16:10:10Z"},{"alias_kind":"pith_short_8","alias_value":"UDGACMIP","created_at":"2026-06-19T16:10:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:UDGACMIPUTS3ZY65RC6HQ3ZYN5","target":"record","payload":{"canonical_record":{"source":{"id":"2606.17356","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-15T23:11:38Z","cross_cats_sorted":[],"title_canon_sha256":"6d1c919f613a4917c5f79de6984c81801e9ab91ed166e0e64ac32bffddef08a2","abstract_canon_sha256":"97acdf485127b6f30dbab641f9e52c94b11ede899cc7aaad46982ed981502903"},"schema_version":"1.0"},"canonical_sha256":"a0cc01310fa4e5bce3dd88bc786f386f799ff03ff98f42e73253d454bc8d01c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:10.022403Z","signature_b64":"V4K251X0CLywzBoxLg9BOms/x0xfTTIEIk7tZ7nQgTcKcbegpGwOtNEQsFi3TyV9ZbsgQC/lQWKjoy98aztDDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0cc01310fa4e5bce3dd88bc786f386f799ff03ff98f42e73253d454bc8d01c4","last_reissued_at":"2026-06-19T16:10:10.021990Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:10.021990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.17356","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":"2026-06-19T16:10:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hq4wnS15RE5BeCv9R2J3ET08KZ0wzdHI3D4DYPHd+fEYNmXGkIYiDSPxuyLEj407dSCPMxX1Sg/iq+kds0UcAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T08:15:27.372487Z"},"content_sha256":"82fe238f51cd7b374347dcea88247bd8ef7f38d72853f7a54edbdb17035fc30e","schema_version":"1.0","event_id":"sha256:82fe238f51cd7b374347dcea88247bd8ef7f38d72853f7a54edbdb17035fc30e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:UDGACMIPUTS3ZY65RC6HQ3ZYN5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A general framework for inequalities on simple graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"\\'Angel Ch\\'avez, Ludovick Bouthat, Sam Sheng","submitted_at":"2026-06-15T23:11:38Z","abstract_excerpt":"A general framework is developed for deriving sharp inequalities on simple graphs from majorization and Schur-convexity. After establishing majorization relations between the spectrum of an arbitrary graph and the spectra of the complete, complete bipartite, and matching graphs, it is shown that every positive Schur-convex spectral functional yields several sharp inequalities relating $\\lambda_1$, $|\\lambda_n|$, and $\\|G\\|_\\ast$. This reduces the problem of proving graph inequalities to the choice of a suitable Schur-convex function. This optimization problem is then studied within the family "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17356","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/2606.17356/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":"2026-06-19T16:10:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E8DVo3WdMZKl9QMo3/Tom3SGvnY6dWzsV2L3Q3oWq+ilVLd92+ceWk8o5jPXMT8H48LJcUDjG4jc9HDCwum/Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T08:15:27.372864Z"},"content_sha256":"4cb35980a78ea2c062c9048ab98f65a79a47c5aada58a4b24b062b0d69e850ec","schema_version":"1.0","event_id":"sha256:4cb35980a78ea2c062c9048ab98f65a79a47c5aada58a4b24b062b0d69e850ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UDGACMIPUTS3ZY65RC6HQ3ZYN5/bundle.json","state_url":"https://pith.science/pith/UDGACMIPUTS3ZY65RC6HQ3ZYN5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UDGACMIPUTS3ZY65RC6HQ3ZYN5/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":"2026-06-29T08:15:27Z","links":{"resolver":"https://pith.science/pith/UDGACMIPUTS3ZY65RC6HQ3ZYN5","bundle":"https://pith.science/pith/UDGACMIPUTS3ZY65RC6HQ3ZYN5/bundle.json","state":"https://pith.science/pith/UDGACMIPUTS3ZY65RC6HQ3ZYN5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UDGACMIPUTS3ZY65RC6HQ3ZYN5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:UDGACMIPUTS3ZY65RC6HQ3ZYN5","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":"97acdf485127b6f30dbab641f9e52c94b11ede899cc7aaad46982ed981502903","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-15T23:11:38Z","title_canon_sha256":"6d1c919f613a4917c5f79de6984c81801e9ab91ed166e0e64ac32bffddef08a2"},"schema_version":"1.0","source":{"id":"2606.17356","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.17356","created_at":"2026-06-19T16:10:10Z"},{"alias_kind":"arxiv_version","alias_value":"2606.17356v1","created_at":"2026-06-19T16:10:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17356","created_at":"2026-06-19T16:10:10Z"},{"alias_kind":"pith_short_12","alias_value":"UDGACMIPUTS3","created_at":"2026-06-19T16:10:10Z"},{"alias_kind":"pith_short_16","alias_value":"UDGACMIPUTS3ZY65","created_at":"2026-06-19T16:10:10Z"},{"alias_kind":"pith_short_8","alias_value":"UDGACMIP","created_at":"2026-06-19T16:10:10Z"}],"graph_snapshots":[{"event_id":"sha256:4cb35980a78ea2c062c9048ab98f65a79a47c5aada58a4b24b062b0d69e850ec","target":"graph","created_at":"2026-06-19T16:10:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.17356/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A general framework is developed for deriving sharp inequalities on simple graphs from majorization and Schur-convexity. After establishing majorization relations between the spectrum of an arbitrary graph and the spectra of the complete, complete bipartite, and matching graphs, it is shown that every positive Schur-convex spectral functional yields several sharp inequalities relating $\\lambda_1$, $|\\lambda_n|$, and $\\|G\\|_\\ast$. This reduces the problem of proving graph inequalities to the choice of a suitable Schur-convex function. This optimization problem is then studied within the family ","authors_text":"\\'Angel Ch\\'avez, Ludovick Bouthat, Sam Sheng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-15T23:11:38Z","title":"A general framework for inequalities on simple graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17356","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":"sha256:82fe238f51cd7b374347dcea88247bd8ef7f38d72853f7a54edbdb17035fc30e","target":"record","created_at":"2026-06-19T16:10:10Z","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":"97acdf485127b6f30dbab641f9e52c94b11ede899cc7aaad46982ed981502903","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-15T23:11:38Z","title_canon_sha256":"6d1c919f613a4917c5f79de6984c81801e9ab91ed166e0e64ac32bffddef08a2"},"schema_version":"1.0","source":{"id":"2606.17356","kind":"arxiv","version":1}},"canonical_sha256":"a0cc01310fa4e5bce3dd88bc786f386f799ff03ff98f42e73253d454bc8d01c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0cc01310fa4e5bce3dd88bc786f386f799ff03ff98f42e73253d454bc8d01c4","first_computed_at":"2026-06-19T16:10:10.021990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:10.021990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V4K251X0CLywzBoxLg9BOms/x0xfTTIEIk7tZ7nQgTcKcbegpGwOtNEQsFi3TyV9ZbsgQC/lQWKjoy98aztDDQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:10.022403Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.17356","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82fe238f51cd7b374347dcea88247bd8ef7f38d72853f7a54edbdb17035fc30e","sha256:4cb35980a78ea2c062c9048ab98f65a79a47c5aada58a4b24b062b0d69e850ec"],"state_sha256":"624d2a7edb3b7cd7a178d30c456eb85d016073658145a336395bcb1e0898041c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Py/HZSaMY601y3sUNjWAYNSac0FybZmvkKTYdpqP8tyj1Mbis9IIO8PjyKFg4o60iuVEsUrbz4JZbKHUQG4Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T08:15:27.374772Z","bundle_sha256":"cc2634de9258755928a7c2e84b4ac9b8ac912a3431a13076407c2c895a0375dd"}}