Pith Number

pith:XKIQAGZS

pith:2012:XKIQAGZSSMOYEQ6T3EWXNYEYT5

not attested not anchored not stored refs pending

An upper gradient approach to weakly differentiable cochains

Kai Rajala, Stefan Wenger

arxiv:1208.4350 v1 · 2012-08-21 · math.AP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XKIQAGZSSMOYEQ6T3EWXNYEYT5}

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	2026-05-18T03:48:23.808600Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba91001b32931d8243d3d92d76e0989f71650882af158337949dca4245085299

Aliases

arxiv: 1208.4350 · arxiv_version: 1208.4350v1 · doi: 10.48550/arxiv.1208.4350 · pith_short_12: XKIQAGZSSMOY · pith_short_16: XKIQAGZSSMOYEQ6T · pith_short_8: XKIQAGZS

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/XKIQAGZSSMOYEQ6T3EWXNYEYT5 \
  | 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: ba91001b32931d8243d3d92d76e0989f71650882af158337949dca4245085299

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "92a7cb838d09c31fe07af358a280aff0e1290401484a6855cc5ad9deae133c84",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-08-21T19:37:02Z",
    "title_canon_sha256": "22646b644c753146b6caeee185aea5ad8696e759294fc8679696159b0c4c5d63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.4350",
    "kind": "arxiv",
    "version": 1
  }
}