Pith Number

pith:4DPXJZDK

pith:2015:4DPXJZDK2BRHHDEKIAOQBABDK3

not attested not anchored not stored refs pending

Quasisymmetric extension on the real line

Vyron Vellis

arxiv:1509.06638 v4 · 2015-09-22 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4DPXJZDK2BRHHDEKIAOQBABDK3}

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	2026-05-18T01:11:55.028774Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0df74e46ad062738c8a401d00802356d0289bfdc142c6a36178e333c9578352

Aliases

arxiv: 1509.06638 · arxiv_version: 1509.06638v4 · doi: 10.48550/arxiv.1509.06638 · pith_short_12: 4DPXJZDK2BRH · pith_short_16: 4DPXJZDK2BRHHDEK · pith_short_8: 4DPXJZDK

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/4DPXJZDK2BRHHDEKIAOQBABDK3 \
  | 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: e0df74e46ad062738c8a401d00802356d0289bfdc142c6a36178e333c9578352

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dea133b2f46b409144856e79007b3bbf67e761b8336c5fbf6bf7b1c551c93f32",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2015-09-22T15:19:06Z",
    "title_canon_sha256": "b59bd60d79a0683aea30e56e6876ede437e6c7fd13a38d5ed84266f9bc1a5a32"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.06638",
    "kind": "arxiv",
    "version": 4
  }
}