FA-99271 / Distributed training aggregation / Open access

A missing parameter shard silently shortens reconstruction · case 01

A missing parameter shard silently shortens reconstruction.

Verified by executionVariant 1 · 6 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Concatenation alone cannot distinguish a complete tensor from a transfer with a gap.

THE FAILURE

Concatenation alone cannot distinguish a complete tensor from a transfer with a gap.

Unsuccessful approach: Checking only the final covered length accepts interior gaps paired with overlaps.

Case contract

Given shards [start, values] and total length, return concatenated values only when intervals exactly cover the range once; otherwise None.

Why this case matters

A toy distributed-training contract makes replica and shard contribution rules explicit without claiming framework compatibility or performance.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(shards, total):
    return [v for s,a in sorted(shards) for v in a]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('complete split',solve([[2,[2,3]],[0,[0,1]]],4),[0,1,2,3])
check('interior gap overlap disguise',solve([[0,[0,1,2]],[2,[2,3]]],4),None)
check('leading gap',solve([[1,[1]]],2),None)
check('trailing gap',solve([[0,[0]]],2),None)
check('empty exact tensor',solve([],0),[])
check('empty with expected values',solve([],1),None)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
complete split	`[0, 1, 2, 3]`	`[0, 1, 2, 3]`	Passed
interior gap overlap disguise	`[0, 1, 2, 2, 3]`	`None`	Failed
leading gap	`[1]`	`None`	Failed
trailing gap	`[0]`	`None`	Failed
empty exact tensor	`[]`	`[]`	Passed
empty with expected values	`[]`	`None`	Failed

SHA-256 / 7fbf4630d31e7cfc594a6a55ae47fd807f45f2513e27287d0f7059a87a8540c1

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(shards, total):
    out=[]; end=0
    for s,a in sorted(shards):
        if s<end: return None
        out.extend(a); end=s+len(a)
    return out if end==total else None
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('complete split',solve([[2,[2,3]],[0,[0,1]]],4),[0,1,2,3])
check('interior gap overlap disguise',solve([[0,[0,1,2]],[2,[2,3]]],4),None)
check('leading gap',solve([[1,[1]]],2),None)
check('trailing gap',solve([[0,[0]]],2),None)
check('empty exact tensor',solve([],0),[])
check('empty with expected values',solve([],1),None)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
complete split	`[0, 1, 2, 3]`	`[0, 1, 2, 3]`	Passed
interior gap overlap disguise	`None`	`None`	Passed
leading gap	`[1]`	`None`	Failed
trailing gap	`None`	`None`	Passed
empty exact tensor	`[]`	`[]`	Passed
empty with expected values	`None`	`None`	Passed

SHA-256 / 43899a2e8e6f90c74897b1c6c582744e9e57fc79813980941ff204a5caf4a9eb

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 6 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

Verification & scope

Inputs are already materialized Python values from a fixed toy collective; no transport, failure recovery, optimizer state, or real model behavior is represented. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-30T16:48:22.178703+00:00.

Case digest / 1bcc1a2757f3b57bf7d19ebada483cbd5cda092456a4061b726b4d54959a1584