Pith Number

pith:HH6UEIQP

pith:2026:HH6UEIQPSNNW7SWIYPTLDXNJNX

not attested not anchored not stored refs pending

Exponential Lower Bounds for the Pfaffian Number of Graphs

Priyanshu Pant, Ranveer Singh

arxiv:2605.21077 v1 · 2026-05-20 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HH6UEIQPSNNW7SWIYPTLDXNJNX}

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	2026-05-21T01:05:35.501202Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

39fd42220f935b6fcac8c3e6b1dda96dd1d68a4e6e6c52d958300b2889485746

Aliases

arxiv: 2605.21077 · arxiv_version: 2605.21077v1 · doi: 10.48550/arxiv.2605.21077 · pith_short_12: HH6UEIQPSNNW · pith_short_16: HH6UEIQPSNNW7SWI · pith_short_8: HH6UEIQP

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/HH6UEIQPSNNW7SWIYPTLDXNJNX \
  | 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: 39fd42220f935b6fcac8c3e6b1dda96dd1d68a4e6e6c52d958300b2889485746

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "101cb878473afa42f52a17ab2a7b95151ec387895203a44c8f26fe8f357a93fc",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-20T12:11:45Z",
    "title_canon_sha256": "dd5d2ef55b1aa46a94b1d1bcd545ca8a620435043081fde9aefca82b65404d55"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.21077",
    "kind": "arxiv",
    "version": 1
  }
}