{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:MRNU3QMHSDOR3YMGEFTN2ITGPF","short_pith_number":"pith:MRNU3QMH","canonical_record":{"source":{"id":"1406.6403","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-06-24T22:29:47Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"66481a225fb1b26a319550a87544ea5a277e38848f3346118682667ca2ee965c","abstract_canon_sha256":"db79da97f89d7706a789335a10ea05b224b2f2fd152000214f49a86126b7b5b2"},"schema_version":"1.0"},"canonical_sha256":"645b4dc18790dd1de1862166dd2266796b1e0b5666dc9366a2176517a36b27d9","source":{"kind":"arxiv","id":"1406.6403","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.6403","created_at":"2026-05-18T02:49:02Z"},{"alias_kind":"arxiv_version","alias_value":"1406.6403v1","created_at":"2026-05-18T02:49:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.6403","created_at":"2026-05-18T02:49:02Z"},{"alias_kind":"pith_short_12","alias_value":"MRNU3QMHSDOR","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MRNU3QMHSDOR3YMG","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MRNU3QMH","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:MRNU3QMHSDOR3YMGEFTN2ITGPF","target":"record","payload":{"canonical_record":{"source":{"id":"1406.6403","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-06-24T22:29:47Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"66481a225fb1b26a319550a87544ea5a277e38848f3346118682667ca2ee965c","abstract_canon_sha256":"db79da97f89d7706a789335a10ea05b224b2f2fd152000214f49a86126b7b5b2"},"schema_version":"1.0"},"canonical_sha256":"645b4dc18790dd1de1862166dd2266796b1e0b5666dc9366a2176517a36b27d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:02.877433Z","signature_b64":"tfBwL/zP+fgWyoMq0CVHoF2InzBPnMFdXN3UwrdEzd+N6ON9jjB26HTgc3jMjS5EpI4qK7K9YEs4ulPNAo8xDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"645b4dc18790dd1de1862166dd2266796b1e0b5666dc9366a2176517a36b27d9","last_reissued_at":"2026-05-18T02:49:02.876973Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:02.876973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.6403","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:49:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bLZmF7NPJCHMngJGByHIa2V2uih3QFOXSXNmxtezU4rlCCBmA7zq445orfZmvGSm9YrEZpFZJy9gUp2DChtIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T02:19:41.892224Z"},"content_sha256":"362b39a12053052febf69cd4423e6bc50ec2d896ffb69202e1f689f1a22f7523","schema_version":"1.0","event_id":"sha256:362b39a12053052febf69cd4423e6bc50ec2d896ffb69202e1f689f1a22f7523"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:MRNU3QMHSDOR3YMGEFTN2ITGPF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An eigenspace approach to isotypic projections for data on binary trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Nathaniel Eldredge","submitted_at":"2014-06-24T22:29:47Z","abstract_excerpt":"The classical Fourier transform is, in essence, a way to take data and extract components (in the form of complex exponentials) which are invariant under cyclic shifts. We consider a case in which the components must instead be invariant under automorphisms of a binary tree. We present a technique by which a slightly relaxed form of the generalized Fourier transform in this case can eventually be computed using only simple tools from linear algebra, which has possible advantages in computational efficiency."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6403","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:49:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ULkTKJy+tFugzzlLprcbobddkjqNN0s4fhgFVJi1sNLy5qJjn681xUw8xOjhdxMgj6w8bDaE+PPywIuCcjkiAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T02:19:41.892900Z"},"content_sha256":"49dcbe65fb450104979f21febca8198296942ca35f1ee0603b8c5aa25b0865e7","schema_version":"1.0","event_id":"sha256:49dcbe65fb450104979f21febca8198296942ca35f1ee0603b8c5aa25b0865e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MRNU3QMHSDOR3YMGEFTN2ITGPF/bundle.json","state_url":"https://pith.science/pith/MRNU3QMHSDOR3YMGEFTN2ITGPF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MRNU3QMHSDOR3YMGEFTN2ITGPF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-12T02:19:41Z","links":{"resolver":"https://pith.science/pith/MRNU3QMHSDOR3YMGEFTN2ITGPF","bundle":"https://pith.science/pith/MRNU3QMHSDOR3YMGEFTN2ITGPF/bundle.json","state":"https://pith.science/pith/MRNU3QMHSDOR3YMGEFTN2ITGPF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MRNU3QMHSDOR3YMGEFTN2ITGPF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MRNU3QMHSDOR3YMGEFTN2ITGPF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"db79da97f89d7706a789335a10ea05b224b2f2fd152000214f49a86126b7b5b2","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-06-24T22:29:47Z","title_canon_sha256":"66481a225fb1b26a319550a87544ea5a277e38848f3346118682667ca2ee965c"},"schema_version":"1.0","source":{"id":"1406.6403","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.6403","created_at":"2026-05-18T02:49:02Z"},{"alias_kind":"arxiv_version","alias_value":"1406.6403v1","created_at":"2026-05-18T02:49:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.6403","created_at":"2026-05-18T02:49:02Z"},{"alias_kind":"pith_short_12","alias_value":"MRNU3QMHSDOR","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MRNU3QMHSDOR3YMG","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MRNU3QMH","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:49dcbe65fb450104979f21febca8198296942ca35f1ee0603b8c5aa25b0865e7","target":"graph","created_at":"2026-05-18T02:49:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The classical Fourier transform is, in essence, a way to take data and extract components (in the form of complex exponentials) which are invariant under cyclic shifts. We consider a case in which the components must instead be invariant under automorphisms of a binary tree. We present a technique by which a slightly relaxed form of the generalized Fourier transform in this case can eventually be computed using only simple tools from linear algebra, which has possible advantages in computational efficiency.","authors_text":"Nathaniel Eldredge","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-06-24T22:29:47Z","title":"An eigenspace approach to isotypic projections for data on binary trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6403","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:362b39a12053052febf69cd4423e6bc50ec2d896ffb69202e1f689f1a22f7523","target":"record","created_at":"2026-05-18T02:49:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"db79da97f89d7706a789335a10ea05b224b2f2fd152000214f49a86126b7b5b2","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-06-24T22:29:47Z","title_canon_sha256":"66481a225fb1b26a319550a87544ea5a277e38848f3346118682667ca2ee965c"},"schema_version":"1.0","source":{"id":"1406.6403","kind":"arxiv","version":1}},"canonical_sha256":"645b4dc18790dd1de1862166dd2266796b1e0b5666dc9366a2176517a36b27d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"645b4dc18790dd1de1862166dd2266796b1e0b5666dc9366a2176517a36b27d9","first_computed_at":"2026-05-18T02:49:02.876973Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:02.876973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tfBwL/zP+fgWyoMq0CVHoF2InzBPnMFdXN3UwrdEzd+N6ON9jjB26HTgc3jMjS5EpI4qK7K9YEs4ulPNAo8xDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:02.877433Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.6403","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:362b39a12053052febf69cd4423e6bc50ec2d896ffb69202e1f689f1a22f7523","sha256:49dcbe65fb450104979f21febca8198296942ca35f1ee0603b8c5aa25b0865e7"],"state_sha256":"b91d08206decec53f0092bf53c4ce841df1b33ac82661502b5663b7661aa34fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MJE5S5ACN5d0Amr9SDwBz1O0rL3KKV0gX2dAxff78znQ92vGo6xcnBMGRGQHtbeVkKS/9/myu3BAtzQd+3gwBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T02:19:41.897577Z","bundle_sha256":"c860805b797146df29cc969eab8312c86d20bb16485b94d74dd755bbd62db437"}}