Pith Number

pith:VV2GQW4B

pith:2011:VV2GQW4BWLVSYLZRXSX72TCNK7

not attested not anchored not stored refs pending

On the 3-$\gamma_t$-Critical Graphs of Order $\Delta(G)+3$

Haoli Wang, Lei Wang, Xirong Xu, Yang Yuansheng

arxiv:1103.2415 v1 · 2011-03-12 · 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{VV2GQW4BWLVSYLZRXSX72TCNK7}

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	2026-05-18T04:26:55.320583Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad74685b81b2eb2c2f31bcaffd4c4d57dfb929ebce548db7404a06721730089f

Aliases

arxiv: 1103.2415 · arxiv_version: 1103.2415v1 · doi: 10.48550/arxiv.1103.2415 · pith_short_12: VV2GQW4BWLVS · pith_short_16: VV2GQW4BWLVSYLZR · pith_short_8: VV2GQW4B

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/VV2GQW4BWLVSYLZRXSX72TCNK7 \
  | 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: ad74685b81b2eb2c2f31bcaffd4c4d57dfb929ebce548db7404a06721730089f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eec4fe4158fdd3b560604918cabf8584a6367f15d873ebce53a55dd59f5cc0ec",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-03-12T03:38:26Z",
    "title_canon_sha256": "c6ec2c2eb06c03a85a088c856d9580f3438b6432fb5bd6199fbc321e98ca801a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.2415",
    "kind": "arxiv",
    "version": 1
  }
}