Pith Number

pith:5G3PWAEP

pith:2012:5G3PWAEPEVK3YDOGR3WFE2CZO5

not attested not anchored not stored refs pending

Homological and homotopical Dehn functions are different

Aaron Abrams, Noel Brady, Pallavi Dani, Robert Young

arxiv:1205.0308 v1 · 2012-05-02 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5G3PWAEPEVK3YDOGR3WFE2CZO5}

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	2026-05-18T02:57:24.326470Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e9b6fb008f2555bc0dc68eec52685977797ae697ec64b9b316988e38ace167cf

Aliases

arxiv: 1205.0308 · arxiv_version: 1205.0308v1 · doi: 10.48550/arxiv.1205.0308 · pith_short_12: 5G3PWAEPEVK3 · pith_short_16: 5G3PWAEPEVK3YDOG · pith_short_8: 5G3PWAEP

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/5G3PWAEPEVK3YDOGR3WFE2CZO5 \
  | 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: e9b6fb008f2555bc0dc68eec52685977797ae697ec64b9b316988e38ace167cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8dc4303a2cb8ffe62b4bfb2bbfa1d077e3ef7e079d4fcae03dfd7c1b7d9fb43",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-05-02T02:48:25Z",
    "title_canon_sha256": "a001b7ad8282fb6f7c37f93a150332f36a6dabc0c131fbc989f665b0ff55b7ba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.0308",
    "kind": "arxiv",
    "version": 1
  }
}