Pith Number

pith:XTKEHNNR

pith:2013:XTKEHNNR764ZFLJFAGNC7VNBHD

not attested not anchored not stored refs pending

On the Action of Reparametrization Group on the Space of $L_k^p$-maps I

Gang Liu

arxiv:1312.4222 v3 · 2013-12-16 · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XTKEHNNR764ZFLJFAGNC7VNBHD}

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	2026-05-18T03:04:06.065323Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bcd443b5b1ffb992ad25019a2fd5a138d8b5b3dd95207233d496967aaa805d0a

Aliases

arxiv: 1312.4222 · arxiv_version: 1312.4222v3 · doi: 10.48550/arxiv.1312.4222 · pith_short_12: XTKEHNNR764Z · pith_short_16: XTKEHNNR764ZFLJF · pith_short_8: XTKEHNNR

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/XTKEHNNR764ZFLJFAGNC7VNBHD \
  | 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: bcd443b5b1ffb992ad25019a2fd5a138d8b5b3dd95207233d496967aaa805d0a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "847358602d7405344415f6e138137686ba0d4cc2505bc9671dd081fd28fb45a5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2013-12-16T01:37:27Z",
    "title_canon_sha256": "977775df78eaaf8e503d5ae286477e4b0892ca3973c3d0ef6331b9920453796f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.4222",
    "kind": "arxiv",
    "version": 3
  }
}