{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:EVPF6QYG57BTF655J6N542R6OM","short_pith_number":"pith:EVPF6QYG","canonical_record":{"source":{"id":"2607.20427","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2026-05-08T16:55:49Z","cross_cats_sorted":["cs.AI","cs.IT","math.IT"],"title_canon_sha256":"5d6d271091c67d0e13a9a1151a2912603bc3c240b251c3c8d21238733166bfa0","abstract_canon_sha256":"427bdb3761bc1c6ec13ef926645f9852859f8cf0923619596386cb88997a9310"},"schema_version":"1.0"},"canonical_sha256":"255e5f4306efc332fbbd4f9bde6a3e73341f1c5f847b8cf68eff8ddbfba51f11","source":{"kind":"arxiv","id":"2607.20427","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.20427","created_at":"2026-07-24T00:23:14Z"},{"alias_kind":"arxiv_version","alias_value":"2607.20427v1","created_at":"2026-07-24T00:23:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.20427","created_at":"2026-07-24T00:23:14Z"},{"alias_kind":"pith_short_12","alias_value":"EVPF6QYG57BT","created_at":"2026-07-24T00:23:14Z"},{"alias_kind":"pith_short_16","alias_value":"EVPF6QYG57BTF655","created_at":"2026-07-24T00:23:14Z"},{"alias_kind":"pith_short_8","alias_value":"EVPF6QYG","created_at":"2026-07-24T00:23:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:EVPF6QYG57BTF655J6N542R6OM","target":"record","payload":{"canonical_record":{"source":{"id":"2607.20427","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2026-05-08T16:55:49Z","cross_cats_sorted":["cs.AI","cs.IT","math.IT"],"title_canon_sha256":"5d6d271091c67d0e13a9a1151a2912603bc3c240b251c3c8d21238733166bfa0","abstract_canon_sha256":"427bdb3761bc1c6ec13ef926645f9852859f8cf0923619596386cb88997a9310"},"schema_version":"1.0"},"canonical_sha256":"255e5f4306efc332fbbd4f9bde6a3e73341f1c5f847b8cf68eff8ddbfba51f11","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-24T00:23:14.741439Z","signature_b64":"14Wzddj4SvasibQaT+dXTuI1zYijC7ClIkIzpMcIK24JiGKcfUSZpBi7KQV5DeEUbaYhZmy2xFgnrME+BKY6DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"255e5f4306efc332fbbd4f9bde6a3e73341f1c5f847b8cf68eff8ddbfba51f11","last_reissued_at":"2026-07-24T00:23:14.740460Z","signature_status":"signed_v1","first_computed_at":"2026-07-24T00:23:14.740460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.20427","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":"2026-07-24T00:23:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u9bxmZ1Z51KjgY7qgVamg/3VfC6aXIDSTCGliEM5rsLBthilLKkb1lVlgvMY2thUmDwvwywPfv0yIyCKwbbmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T22:55:38.559067Z"},"content_sha256":"a413fc6f8508b4267a60802f5e3b026799b84638c57e6b196b16785af9ccd14c","schema_version":"1.0","event_id":"sha256:a413fc6f8508b4267a60802f5e3b026799b84638c57e6b196b16785af9ccd14c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:EVPF6QYG57BTF655J6N542R6OM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Is MoE Routing a Huffman Code? Discovering the Frequency-Diversity Law in Chain-of-Thought","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.IT","math.IT"],"primary_cat":"cs.CL","authors_text":"Ching-Chieh Tsao, Wenya Wang, Zhuoyi Lin","submitted_at":"2026-05-08T16:55:49Z","abstract_excerpt":"Mixture-of-Experts architectures have revolutionized scaling, yet the underlying logic of their routing remains a black box. In this paper, we uncover a fundamental governing principle: MoE routing is not merely selection, but a manifestation of Huffman Coding. We introduce the Frequency-Diversity Law, revealing that state-of-the-art models, such as Phi-3.5-MoE and Gemma-4-27B-A4B, spontaneously act as information-theoretic engines. These models allocate sparse expert resources for common tokens while invoking high-diversity expert committees for rare, complex tasks found in chain-of-thought t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20427","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/2607.20427/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":"2026-07-24T00:23:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a+rw/dnxqSR1DJRiDFPUhc4BtfMKiEIY/rQxRgurnDkJGbSrTL5yHUXGQUhnLdP3aEvnMn7OZcKUeJgmlABmCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T22:55:38.559638Z"},"content_sha256":"22d6137bd58c47ab3f1649f68bb0d4d938563e29c66f95c58ca19b2c5c2c5411","schema_version":"1.0","event_id":"sha256:22d6137bd58c47ab3f1649f68bb0d4d938563e29c66f95c58ca19b2c5c2c5411"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EVPF6QYG57BTF655J6N542R6OM/bundle.json","state_url":"https://pith.science/pith/EVPF6QYG57BTF655J6N542R6OM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EVPF6QYG57BTF655J6N542R6OM/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":"2026-08-03T22:55:38Z","links":{"resolver":"https://pith.science/pith/EVPF6QYG57BTF655J6N542R6OM","bundle":"https://pith.science/pith/EVPF6QYG57BTF655J6N542R6OM/bundle.json","state":"https://pith.science/pith/EVPF6QYG57BTF655J6N542R6OM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EVPF6QYG57BTF655J6N542R6OM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:EVPF6QYG57BTF655J6N542R6OM","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":"427bdb3761bc1c6ec13ef926645f9852859f8cf0923619596386cb88997a9310","cross_cats_sorted":["cs.AI","cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2026-05-08T16:55:49Z","title_canon_sha256":"5d6d271091c67d0e13a9a1151a2912603bc3c240b251c3c8d21238733166bfa0"},"schema_version":"1.0","source":{"id":"2607.20427","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.20427","created_at":"2026-07-24T00:23:14Z"},{"alias_kind":"arxiv_version","alias_value":"2607.20427v1","created_at":"2026-07-24T00:23:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.20427","created_at":"2026-07-24T00:23:14Z"},{"alias_kind":"pith_short_12","alias_value":"EVPF6QYG57BT","created_at":"2026-07-24T00:23:14Z"},{"alias_kind":"pith_short_16","alias_value":"EVPF6QYG57BTF655","created_at":"2026-07-24T00:23:14Z"},{"alias_kind":"pith_short_8","alias_value":"EVPF6QYG","created_at":"2026-07-24T00:23:14Z"}],"graph_snapshots":[{"event_id":"sha256:22d6137bd58c47ab3f1649f68bb0d4d938563e29c66f95c58ca19b2c5c2c5411","target":"graph","created_at":"2026-07-24T00:23:14Z","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/2607.20427/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Mixture-of-Experts architectures have revolutionized scaling, yet the underlying logic of their routing remains a black box. In this paper, we uncover a fundamental governing principle: MoE routing is not merely selection, but a manifestation of Huffman Coding. We introduce the Frequency-Diversity Law, revealing that state-of-the-art models, such as Phi-3.5-MoE and Gemma-4-27B-A4B, spontaneously act as information-theoretic engines. These models allocate sparse expert resources for common tokens while invoking high-diversity expert committees for rare, complex tasks found in chain-of-thought t","authors_text":"Ching-Chieh Tsao, Wenya Wang, Zhuoyi Lin","cross_cats":["cs.AI","cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2026-05-08T16:55:49Z","title":"Is MoE Routing a Huffman Code? Discovering the Frequency-Diversity Law in Chain-of-Thought"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20427","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:a413fc6f8508b4267a60802f5e3b026799b84638c57e6b196b16785af9ccd14c","target":"record","created_at":"2026-07-24T00:23:14Z","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":"427bdb3761bc1c6ec13ef926645f9852859f8cf0923619596386cb88997a9310","cross_cats_sorted":["cs.AI","cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2026-05-08T16:55:49Z","title_canon_sha256":"5d6d271091c67d0e13a9a1151a2912603bc3c240b251c3c8d21238733166bfa0"},"schema_version":"1.0","source":{"id":"2607.20427","kind":"arxiv","version":1}},"canonical_sha256":"255e5f4306efc332fbbd4f9bde6a3e73341f1c5f847b8cf68eff8ddbfba51f11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"255e5f4306efc332fbbd4f9bde6a3e73341f1c5f847b8cf68eff8ddbfba51f11","first_computed_at":"2026-07-24T00:23:14.740460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-24T00:23:14.740460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"14Wzddj4SvasibQaT+dXTuI1zYijC7ClIkIzpMcIK24JiGKcfUSZpBi7KQV5DeEUbaYhZmy2xFgnrME+BKY6DQ==","signature_status":"signed_v1","signed_at":"2026-07-24T00:23:14.741439Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.20427","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a413fc6f8508b4267a60802f5e3b026799b84638c57e6b196b16785af9ccd14c","sha256:22d6137bd58c47ab3f1649f68bb0d4d938563e29c66f95c58ca19b2c5c2c5411"],"state_sha256":"45b20aaada7a17498725435a3f93cfaab44b745a341fe7e6f8970d0f6f14c77d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TlvqdNHHM0JrjkumaQE6RzVsAD33GnRqyGZBZUFjQsfPWTzV/w/52aX+MzHswx51rlVsJxc/v7EpFfkByqiCAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T22:55:38.565612Z","bundle_sha256":"d6a085375b4edaa8c963a6fd45593695f7ffba3cfac9a2f131843a36d7009aa7"}}