Pith Number

pith:FH3OTEI3

pith:2021:FH3OTEI3T4EAOA4N2N2LI2MN3F

not attested not anchored not stored refs pending

The Convexity and Concavity of Envelopes of the Minimum-Relative-Entropy Region for the DSBS

Lei Yu

arxiv:2106.03654 v1 · 2021-06-07 · cs.IT · math.IT · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FH3OTEI3T4EAOA4N2N2LI2MN3F}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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.

Cited by

1 paper in Pith

On the Fundamental Limits of Integrated Sensing and Communications Under Logarithmic Loss

Receipt and verification

First computed	2026-07-05T02:46:51.949027Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

29f6e9911b9f0807038dd374b4698dd95d9bf3aafa497ab7e657ac51b923f401

Aliases

arxiv: 2106.03654 · arxiv_version: 2106.03654v1 · doi: 10.48550/arxiv.2106.03654 · pith_short_12: FH3OTEI3T4EA · pith_short_16: FH3OTEI3T4EAOA4N · pith_short_8: FH3OTEI3

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/FH3OTEI3T4EAOA4N2N2LI2MN3F \
  | 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: 29f6e9911b9f0807038dd374b4698dd95d9bf3aafa497ab7e657ac51b923f401

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f2083477d7952f849f694df83eb070d32428aa4f2f9d556ba996b6b4f5fb163",
    "cross_cats_sorted": [
      "math.IT",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2021-06-07T14:33:25Z",
    "title_canon_sha256": "872d975cc51aabb1bf49bd8438dc3ab58277cfec3d45dc2802734d7c884bc2ee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.03654",
    "kind": "arxiv",
    "version": 1
  }
}