Pith Number

pith:2GKPECRR

pith:2005:2GKPECRR6INYCXJ4LPLHAFA2SB

not attested not anchored not stored refs pending

Self-intersections of Immersions and Steenrod Operations

Mark Grant, Peter J. Eccles

arxiv:math/0509213 v3 · 2005-09-09 · math.AT · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2GKPECRR6INYCXJ4LPLHAFA2SB}

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	2026-05-18T04:12:19.397795Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d194f20a31f21b815d3c5bd670141a906168d672508af33177f68510e277f14c

Aliases

arxiv: math/0509213 · arxiv_version: math/0509213v3 · doi: 10.48550/arxiv.math/0509213 · pith_short_12: 2GKPECRR6INY · pith_short_16: 2GKPECRR6INYCXJ4 · pith_short_8: 2GKPECRR

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/2GKPECRR6INYCXJ4LPLHAFA2SB \
  | 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: d194f20a31f21b815d3c5bd670141a906168d672508af33177f68510e277f14c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86c68095236753c5d483d2547a1d33d5eb78a3c88c45f3f01c6eb3728bdcc7fb",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2005-09-09T15:36:27Z",
    "title_canon_sha256": "f87dc30e4619af0d409d3e9f126712f6a33b109d2870b9c3aae9b7c6cff7e1bd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0509213",
    "kind": "arxiv",
    "version": 3
  }
}