{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:KD46OUBCZYPQBR3V63BV5G6JTQ","short_pith_number":"pith:KD46OUBC","canonical_record":{"source":{"id":"2605.31507","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-05-29T16:26:32Z","cross_cats_sorted":[],"title_canon_sha256":"a13f0128a3c9547244a4a8fdefe80b1d73b480e91b50bcf3dcd97007e77bd366","abstract_canon_sha256":"068ec8307801c41ae847b3a03ef90ab52e8673776e9d5eef422a50d961e6829a"},"schema_version":"1.0"},"canonical_sha256":"50f9e75022ce1f00c775f6c35e9bc99c224d06b285d56660feb4dc0f7283cbfd","source":{"kind":"arxiv","id":"2605.31507","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.31507","created_at":"2026-06-01T02:04:09Z"},{"alias_kind":"arxiv_version","alias_value":"2605.31507v1","created_at":"2026-06-01T02:04:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.31507","created_at":"2026-06-01T02:04:09Z"},{"alias_kind":"pith_short_12","alias_value":"KD46OUBCZYPQ","created_at":"2026-06-01T02:04:09Z"},{"alias_kind":"pith_short_16","alias_value":"KD46OUBCZYPQBR3V","created_at":"2026-06-01T02:04:09Z"},{"alias_kind":"pith_short_8","alias_value":"KD46OUBC","created_at":"2026-06-01T02:04:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:KD46OUBCZYPQBR3V63BV5G6JTQ","target":"record","payload":{"canonical_record":{"source":{"id":"2605.31507","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-05-29T16:26:32Z","cross_cats_sorted":[],"title_canon_sha256":"a13f0128a3c9547244a4a8fdefe80b1d73b480e91b50bcf3dcd97007e77bd366","abstract_canon_sha256":"068ec8307801c41ae847b3a03ef90ab52e8673776e9d5eef422a50d961e6829a"},"schema_version":"1.0"},"canonical_sha256":"50f9e75022ce1f00c775f6c35e9bc99c224d06b285d56660feb4dc0f7283cbfd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-01T02:04:09.863134Z","signature_b64":"nPBIXlv+FVfe5jfjOPUrKkpt2HHq++JELntMsM1lljIKpIQoY33L70R0ZWjFVS1JBfYAJgi8bJtXxviiKgxHAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50f9e75022ce1f00c775f6c35e9bc99c224d06b285d56660feb4dc0f7283cbfd","last_reissued_at":"2026-06-01T02:04:09.862146Z","signature_status":"signed_v1","first_computed_at":"2026-06-01T02:04:09.862146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.31507","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":"2026-06-01T02:04:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dh54wGwhloVFvsMNqxxbld59j5qCDDvwvmwur6tvze9C0SelLLQbMSB8C7i2z6W2LUNhWpiQJWI5virg5VNNAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T20:24:35.969341Z"},"content_sha256":"9293f54747ea3fc73e5a704991aa59294765a2f51e053de6f4e184e44f12e65c","schema_version":"1.0","event_id":"sha256:9293f54747ea3fc73e5a704991aa59294765a2f51e053de6f4e184e44f12e65c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:KD46OUBCZYPQBR3V63BV5G6JTQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uncertainty Principles as a Tool for STFT Phase Retrieval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"David Bartusel","submitted_at":"2026-05-29T16:26:32Z","abstract_excerpt":"In the finite-dimensional setting, it is known that STFT phase retrieval is always possible when the window's ambiguity function does not vanish. However, it is not known how many zeros are allowed in the ambiguity function for the window still to allow phase retrieval. In order to tackle this problem, we first consider a two-window approach where the second window equals the Fourier transform of the first window. This allows us to apply the uncertainty principle in order to obtain sufficient conditions for phase retrieval. Using the relation between STFT phase retrieval and ambiguity sampling"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.31507","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.31507/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-01T02:04:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T1KtpONw2c+bpTCgAhoIODRXzabC5jbl2GE3n7nxwO+6F74dSimsQcRbfJPZ0mNv3dHekXwjS3SljleaKdfYAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T20:24:35.969717Z"},"content_sha256":"71e1d7ce996e9753025fc3db9ed9bdaff59de6ee36caba143451c7144bf5e4d7","schema_version":"1.0","event_id":"sha256:71e1d7ce996e9753025fc3db9ed9bdaff59de6ee36caba143451c7144bf5e4d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KD46OUBCZYPQBR3V63BV5G6JTQ/bundle.json","state_url":"https://pith.science/pith/KD46OUBCZYPQBR3V63BV5G6JTQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KD46OUBCZYPQBR3V63BV5G6JTQ/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":"2026-07-06T20:24:35Z","links":{"resolver":"https://pith.science/pith/KD46OUBCZYPQBR3V63BV5G6JTQ","bundle":"https://pith.science/pith/KD46OUBCZYPQBR3V63BV5G6JTQ/bundle.json","state":"https://pith.science/pith/KD46OUBCZYPQBR3V63BV5G6JTQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KD46OUBCZYPQBR3V63BV5G6JTQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:KD46OUBCZYPQBR3V63BV5G6JTQ","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":"068ec8307801c41ae847b3a03ef90ab52e8673776e9d5eef422a50d961e6829a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-05-29T16:26:32Z","title_canon_sha256":"a13f0128a3c9547244a4a8fdefe80b1d73b480e91b50bcf3dcd97007e77bd366"},"schema_version":"1.0","source":{"id":"2605.31507","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.31507","created_at":"2026-06-01T02:04:09Z"},{"alias_kind":"arxiv_version","alias_value":"2605.31507v1","created_at":"2026-06-01T02:04:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.31507","created_at":"2026-06-01T02:04:09Z"},{"alias_kind":"pith_short_12","alias_value":"KD46OUBCZYPQ","created_at":"2026-06-01T02:04:09Z"},{"alias_kind":"pith_short_16","alias_value":"KD46OUBCZYPQBR3V","created_at":"2026-06-01T02:04:09Z"},{"alias_kind":"pith_short_8","alias_value":"KD46OUBC","created_at":"2026-06-01T02:04:09Z"}],"graph_snapshots":[{"event_id":"sha256:71e1d7ce996e9753025fc3db9ed9bdaff59de6ee36caba143451c7144bf5e4d7","target":"graph","created_at":"2026-06-01T02:04:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.31507/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the finite-dimensional setting, it is known that STFT phase retrieval is always possible when the window's ambiguity function does not vanish. However, it is not known how many zeros are allowed in the ambiguity function for the window still to allow phase retrieval. In order to tackle this problem, we first consider a two-window approach where the second window equals the Fourier transform of the first window. This allows us to apply the uncertainty principle in order to obtain sufficient conditions for phase retrieval. Using the relation between STFT phase retrieval and ambiguity sampling","authors_text":"David Bartusel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-05-29T16:26:32Z","title":"Uncertainty Principles as a Tool for STFT Phase Retrieval"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.31507","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":"sha256:9293f54747ea3fc73e5a704991aa59294765a2f51e053de6f4e184e44f12e65c","target":"record","created_at":"2026-06-01T02:04:09Z","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":"068ec8307801c41ae847b3a03ef90ab52e8673776e9d5eef422a50d961e6829a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-05-29T16:26:32Z","title_canon_sha256":"a13f0128a3c9547244a4a8fdefe80b1d73b480e91b50bcf3dcd97007e77bd366"},"schema_version":"1.0","source":{"id":"2605.31507","kind":"arxiv","version":1}},"canonical_sha256":"50f9e75022ce1f00c775f6c35e9bc99c224d06b285d56660feb4dc0f7283cbfd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50f9e75022ce1f00c775f6c35e9bc99c224d06b285d56660feb4dc0f7283cbfd","first_computed_at":"2026-06-01T02:04:09.862146Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-01T02:04:09.862146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nPBIXlv+FVfe5jfjOPUrKkpt2HHq++JELntMsM1lljIKpIQoY33L70R0ZWjFVS1JBfYAJgi8bJtXxviiKgxHAg==","signature_status":"signed_v1","signed_at":"2026-06-01T02:04:09.863134Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.31507","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9293f54747ea3fc73e5a704991aa59294765a2f51e053de6f4e184e44f12e65c","sha256:71e1d7ce996e9753025fc3db9ed9bdaff59de6ee36caba143451c7144bf5e4d7"],"state_sha256":"dfabec6c7beb27151c7be01fc00edf15464ed6fbe2d0f416b5435cab852a89ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l27lriKXnjw9VPWi+yoaEeHeFztFKgwPkmXpiCRv/PtsGMopxAm7mjo9tpr7pTzikixuciX8jbDSJaFPhouLDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T20:24:35.971643Z","bundle_sha256":"df3b56b1146a6a716c2b4caf218750cabbc2cbf8e4488c5f3967d5203397899b"}}