Pith Number

pith:ATD5SWZ2

pith:2008:ATD5SWZ2YPDL67LXQTUVGAQVGW

not attested not anchored not stored refs pending

Invariant boundary distributions for finite graphs

Guyan Robertson

arxiv:0801.0667 v2 · 2008-01-04 · math.GR · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ATD5SWZ2YPDL67LXQTUVGAQVGW}

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	2026-05-18T03:32:57.657391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04c7d95b3ac3c6bf7d7784e953021535b9711c81e86f3a428efadafc1d386159

Aliases

arxiv: 0801.0667 · arxiv_version: 0801.0667v2 · doi: 10.48550/arxiv.0801.0667 · pith_short_12: ATD5SWZ2YPDL · pith_short_16: ATD5SWZ2YPDL67LX · pith_short_8: ATD5SWZ2

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/ATD5SWZ2YPDL67LXQTUVGAQVGW \
  | 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: 04c7d95b3ac3c6bf7d7784e953021535b9711c81e86f3a428efadafc1d386159

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb15c80a3f9d8dc97f1f287ed40d084073aed06fe5c4003792f09b863485fe41",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2008-01-04T12:00:41Z",
    "title_canon_sha256": "595eaa267c5d2ebac869a8c3818537df8a6092f18a91366ab6ac77cd623cd9ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0801.0667",
    "kind": "arxiv",
    "version": 2
  }
}