Pith Number

pith:SMIYT6JF

pith:2026:SMIYT6JF3RT33IL33OCLGSRXKV

not attested not anchored not stored refs pending

Where Hindsight Credit Can Reside: A Signed-Capacity View of Token Updates in RLVR

Hange Zhou, Haodong Wu, Hongyu Ge, Keyi Wu, Qihong Lin, Siyi Liu, Yongqi Zhang, Yuhang He, Zhuo Zheng, Zixin Zhong

The credit a token can carry in RLVR is upper-bounded by its entropy.

arxiv:2604.11056 v2 · 2026-04-13 · cs.LG · cs.AI

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\usepackage{pith}
\pithnumber{SMIYT6JF3RT33IL33OCLGSRXKV}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We adapt Conditional Mutual Information to the autoregressive RLVR setting and prove that the credit a token can carry is upper-bounded by its entropy.

C2weakest assumption

The adaptation of conditional mutual information to the autoregressive RLVR setting correctly captures the credit a token can carry, and that high-entropy tokens are the primary locus of reasoning improvements.

C3one line summary

Token credit in RLVR is upper-bounded by entropy, with reasoning gains concentrated in high-entropy tokens, motivating Entropy-Aware Policy Optimization that outperforms baselines.

Formal links

2 machine-checked theorem links

Cited by

3 papers in Pith

Tailoring Teaching to Aptitude: Direction-Adaptive Self-Distillation for LLM Reasoning

From Instance Selection to Fixed-Pool Data Recipe Search for Supervised Fine-Tuning

Not All Tokens Learn Alike: Attention Entropy Reveals Heterogeneous Signals in RL Reasoning

Receipt and verification

First computed	2026-05-27T01:05:54.301633Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

931189f925dc67bda17bdb84b34a3755589b0d877512ba1d10f86db0cb49d7d3

Aliases

arxiv: 2604.11056 · arxiv_version: 2604.11056v2 · doi: 10.48550/arxiv.2604.11056 · pith_short_12: SMIYT6JF3RT3 · pith_short_16: SMIYT6JF3RT33IL3 · pith_short_8: SMIYT6JF

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SMIYT6JF3RT33IL33OCLGSRXKV \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 931189f925dc67bda17bdb84b34a3755589b0d877512ba1d10f86db0cb49d7d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec7e168f367dde92704456449ca2533fa1aa887dd58db9ffcba34e5a2d3477eb",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-04-13T06:32:49Z",
    "title_canon_sha256": "b19507d8506e7f744dae6da2c1140f931113ce7594dd9cc78600704295f35401"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.11056",
    "kind": "arxiv",
    "version": 2
  }
}