Pith Number

pith:42PJNF3Y

pith:2026:42PJNF3YYXGPBFBJUWJN7DNWKM

not attested not anchored not stored refs pending

Asymmetric induced saturation

Sahab Hajebi, Sepehr Hajebi, Sophie Spirkl, Xinyue Fan

arxiv:2606.24763 v1 · 2026-06-23 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{42PJNF3YYXGPBFBJUWJN7DNWKM}

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.

Receipt and verification

First computed	2026-06-24T01:15:41.572399Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e69e969778c5ccf09429a592df8db6530e43bdbb4482e486f9a1ea5677c5e45a

Aliases

arxiv: 2606.24763 · arxiv_version: 2606.24763v1 · doi: 10.48550/arxiv.2606.24763 · pith_short_12: 42PJNF3YYXGP · pith_short_16: 42PJNF3YYXGPBFBJ · pith_short_8: 42PJNF3Y

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/42PJNF3YYXGPBFBJUWJN7DNWKM \
  | 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: e69e969778c5ccf09429a592df8db6530e43bdbb4482e486f9a1ea5677c5e45a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a83f7b3b7905575b319034000facc6eccd96748c61a7097da6b1b1b736ac747",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-23T16:20:18Z",
    "title_canon_sha256": "37fb0b4a1bf531ab2249f5a54ac44a0ce851237694c65948e00bec52076b0a89"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.24763",
    "kind": "arxiv",
    "version": 1
  }
}