Pith Number

pith:YFIZE6ZB

pith:2026:YFIZE6ZBISRID55MX3SY6CM4IJ

not attested not anchored not stored refs pending

How are linear representations learned? Exact solutions to the dynamics of abstraction

Andrew M. Saxe, Peter E. Latham, William W. Yang

arxiv:2607.08843 v1 · 2026-07-09 · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YFIZE6ZBISRID55MX3SY6CM4IJ}

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	2026-07-13T00:17:21.519194Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c151927b2144a281f7acbee58f099c42540e7c1973c8709544a104fa51d127dc

Aliases

arxiv: 2607.08843 · arxiv_version: 2607.08843v1 · doi: 10.48550/arxiv.2607.08843 · pith_short_12: YFIZE6ZBISRI · pith_short_16: YFIZE6ZBISRID55M · pith_short_8: YFIZE6ZB

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/YFIZE6ZBISRID55MX3SY6CM4IJ \
  | 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: c151927b2144a281f7acbee58f099c42540e7c1973c8709544a104fa51d127dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "30360fa4598f30bb32408f10af6593775b0f70e23d0245040613255c7e11fb39",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-09T18:04:25Z",
    "title_canon_sha256": "e44e48ce10f1505b843b58d66524e5f9577d1351907400f3a942a4bee0adc33a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.08843",
    "kind": "arxiv",
    "version": 1
  }
}