Pith Number

pith:PKQBYHQ5

pith:2026:PKQBYHQ5MIBOJHPNVT2CCNO7IV

not attested not anchored not stored refs pending

Sublinear projection tracking in acylindrically hyperbolic groups

Lihuang Ding, Wenyuan Yang

arxiv:2607.25555 v1 · 2026-07-28 · math.GR · 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{PKQBYHQ5MIBOJHPNVT2CCNO7IV}

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	2026-07-29T01:25:46.606679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7aa01c1e1d6202e49dedacf42135df454838a521ad155136d47ca92728b44541

Aliases

arxiv: 2607.25555 · arxiv_version: 2607.25555v1 · doi: 10.48550/arxiv.2607.25555 · pith_short_12: PKQBYHQ5MIBO · pith_short_16: PKQBYHQ5MIBOJHPN · pith_short_8: PKQBYHQ5

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/PKQBYHQ5MIBOJHPNVT2CCNO7IV \
  | 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: 7aa01c1e1d6202e49dedacf42135df454838a521ad155136d47ca92728b44541

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09d7dbef102a897a1bf89282f748dd9539510d042e9833bb32d68a0ac82e86ec",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-07-28T10:37:06Z",
    "title_canon_sha256": "1c73b2cc1cc556439810b905a36768b2cc21a7294995bb00f50c4a25f6117717"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.25555",
    "kind": "arxiv",
    "version": 1
  }
}