Pith Number

pith:WN3LFTJL

pith:2007:WN3LFTJLJ2KZBNQ3AS4GFEYTFG

not attested not anchored not stored refs pending

Duality for topological abelian group stacks and T-duality

Andreas Thom, Markus Spitzweck, Thomas Schick, Ulrich Bunke

arxiv:math/0701428 v2 · 2007-01-15 · math.AT · 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{WN3LFTJLJ2KZBNQ3AS4GFEYTFG}

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	2026-05-17T23:59:44.846187Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b376b2cd2b4e9590b61b04b862931329a5126093f0bab2a5c272eefb35d326ec

Aliases

arxiv: math/0701428 · arxiv_version: math/0701428v2 · doi: 10.48550/arxiv.math/0701428 · pith_short_12: WN3LFTJLJ2KZ · pith_short_16: WN3LFTJLJ2KZBNQ3 · pith_short_8: WN3LFTJL

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/WN3LFTJLJ2KZBNQ3AS4GFEYTFG \
  | 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: b376b2cd2b4e9590b61b04b862931329a5126093f0bab2a5c272eefb35d326ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fced38041c01a67ce90b7ac698ec6542e3de1e85418b6e8547272e526acbed0d",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.AT",
    "submitted_at": "2007-01-15T22:46:57Z",
    "title_canon_sha256": "00043f4714faf95dd798555c326e63b71ca3b6119c3cb098c44e18ee48d6c229"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0701428",
    "kind": "arxiv",
    "version": 2
  }
}