Pith Number

pith:5JPYQB2I

pith:2013:5JPYQB2IOVNP4QPA5AEWNL6MP2

not attested not anchored not stored refs pending

Quadratic Bounds on the Quasiconvexity of Nested Train Track Sequences

Tarik Aougab

arxiv:1306.1428 v2 · 2013-06-06 · 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{5JPYQB2IOVNP4QPA5AEWNL6MP2}

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	2026-05-18T03:21:33.140501Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea5f880748755afe41e0e80966afcc7e9e214ee967f2d47d03f4a2e6b8796218

Aliases

arxiv: 1306.1428 · arxiv_version: 1306.1428v2 · doi: 10.48550/arxiv.1306.1428 · pith_short_12: 5JPYQB2IOVNP · pith_short_16: 5JPYQB2IOVNP4QPA · pith_short_8: 5JPYQB2I

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/5JPYQB2IOVNP4QPA5AEWNL6MP2 \
  | 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: ea5f880748755afe41e0e80966afcc7e9e214ee967f2d47d03f4a2e6b8796218

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f12d7efcab37cd9c35771a1e73d4ca505065443e5edb849f709d1e9d206312f4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-06-06T15:09:56Z",
    "title_canon_sha256": "063d3323a93886d651f5701bf05900786810ec0e816897461c82beef8345428f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.1428",
    "kind": "arxiv",
    "version": 2
  }
}