Pith Number

pith:EDG25XSC

pith:2016:EDG25XSCJGC2CJLWYO7ZE6LRY5

not attested not anchored not stored refs pending

Dual Immaculate Quasisymmetric Functions Expand Positively into Young Quasisymmetric Schur Functions

Edward E. Allen, Joshua Hallam, Sarah K. Mason

arxiv:1606.03519 v1 · 2016-06-11 · 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{EDG25XSCJGC2CJLWYO7ZE6LRY5}

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	2026-05-18T01:12:33.846130Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

20cdaede424985a12576c3bf927971c75f958c129f3d34e3e421cd0b91c6c4ea

Aliases

arxiv: 1606.03519 · arxiv_version: 1606.03519v1 · doi: 10.48550/arxiv.1606.03519 · pith_short_12: EDG25XSCJGC2 · pith_short_16: EDG25XSCJGC2CJLW · pith_short_8: EDG25XSC

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/EDG25XSCJGC2CJLWYO7ZE6LRY5 \
  | 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: 20cdaede424985a12576c3bf927971c75f958c129f3d34e3e421cd0b91c6c4ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6d6971cb2cf78ac308a7e5f4f4afb7ddfe607b34e1670b162ff57dcf944e2ea",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-06-11T01:24:00Z",
    "title_canon_sha256": "5065ceb7c405fb205fc3cb5cd810809f1958164975d09f89f4bc928b99817c56"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.03519",
    "kind": "arxiv",
    "version": 1
  }
}