Pith Number

pith:PHXHPAIY

pith:2015:PHXHPAIYUWFAAYVCB7WHRY5VZJ

not attested not anchored not stored refs pending

A proof of the shuffle conjecture

Anton Mellit, Erik Carlsson

arxiv:1508.06239 v3 · 2015-08-25 · math.RT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PHXHPAIYUWFAAYVCB7WHRY5VZJ}

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	2026-05-17T23:58:50.652784Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79ee778118a58a0062a20fec78e3b5ca696b035b075323d505acb890c458dc64

Aliases

arxiv: 1508.06239 · arxiv_version: 1508.06239v3 · doi: 10.48550/arxiv.1508.06239 · pith_short_12: PHXHPAIYUWFA · pith_short_16: PHXHPAIYUWFAAYVC · pith_short_8: PHXHPAIY

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/PHXHPAIYUWFAAYVCB7WHRY5VZJ \
  | 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: 79ee778118a58a0062a20fec78e3b5ca696b035b075323d505acb890c458dc64

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05255a2cc1cc1842a601c41ce48218b10103cbec7b61fc94c3bca8eb3d5aff8c",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2015-08-25T18:21:23Z",
    "title_canon_sha256": "f715b20264a6535e4ac2a956137e0c6cb5fb3ea4d9016380f0917950de34e22c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.06239",
    "kind": "arxiv",
    "version": 3
  }
}