Pith Number

pith:6MQIP2WS

pith:2025:6MQIP2WSWRMGGWUAWO4VGD6JM2

not attested not anchored not stored refs pending

Sums along the edges of bounded degree graphs

Georgii Zakharov, Itai Benjamini, Maksim Zhukovskii, Noga Alon

arxiv:2507.01138 v2 · 2025-07-01 · 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{6MQIP2WSWRMGGWUAWO4VGD6JM2}

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

Universality in random graphs via optimal linking systems: trees and beyond

Receipt and verification

First computed	2026-07-05T11:46:44.712642Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f32087ead2b458635a80b3b9530fc966bf5bce979c1bf7fe0b54861dfdd5ad21

Aliases

arxiv: 2507.01138 · arxiv_version: 2507.01138v2 · doi: 10.48550/arxiv.2507.01138 · pith_short_12: 6MQIP2WSWRMG · pith_short_16: 6MQIP2WSWRMGGWUA · pith_short_8: 6MQIP2WS

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/6MQIP2WSWRMGGWUAWO4VGD6JM2 \
  | 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: f32087ead2b458635a80b3b9530fc966bf5bce979c1bf7fe0b54861dfdd5ad21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c56c3aa49f5068004efe2c4364b4f48c51be18c38adbb77ce5e4f7663119ff0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-01T18:56:07Z",
    "title_canon_sha256": "ac148726b482571765c875b3b74473bbbb83bf06246fb6693161388947b4e833"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.01138",
    "kind": "arxiv",
    "version": 2
  }
}