{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:35IGKJUXVHTC24S5OCU37QIOTZ","short_pith_number":"pith:35IGKJUX","canonical_record":{"source":{"id":"1001.3910","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-01-22T03:31:30Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"1f62a1488a4b7d2da803192de51d43cc73cd211d227615ab38c4beb2cbf370f4","abstract_canon_sha256":"8e126c9960fc9d8e037bafc8d4b88e6623b92f9cb8a38f2710650c6d283c97e0"},"schema_version":"1.0"},"canonical_sha256":"df50652697a9e62d725d70a9bfc10e9e44933cbd24cd5fadf208769a07b7ce94","source":{"kind":"arxiv","id":"1001.3910","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.3910","created_at":"2026-05-18T03:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1001.3910v2","created_at":"2026-05-18T03:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.3910","created_at":"2026-05-18T03:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"35IGKJUXVHTC","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"35IGKJUXVHTC24S5","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"35IGKJUX","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:35IGKJUXVHTC24S5OCU37QIOTZ","target":"record","payload":{"canonical_record":{"source":{"id":"1001.3910","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-01-22T03:31:30Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"1f62a1488a4b7d2da803192de51d43cc73cd211d227615ab38c4beb2cbf370f4","abstract_canon_sha256":"8e126c9960fc9d8e037bafc8d4b88e6623b92f9cb8a38f2710650c6d283c97e0"},"schema_version":"1.0"},"canonical_sha256":"df50652697a9e62d725d70a9bfc10e9e44933cbd24cd5fadf208769a07b7ce94","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:12.673151Z","signature_b64":"fgDmGGVp+pDAqLEOCPntEBUfhXAGitUHqGdaVl1/fyil0YtH0p0ThqC75ms44LEiVUx1tMiwo/tCFmWoCQsHAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df50652697a9e62d725d70a9bfc10e9e44933cbd24cd5fadf208769a07b7ce94","last_reissued_at":"2026-05-18T03:52:12.672535Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:12.672535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.3910","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2glOEY8WzQxKvtt/w3FHMLd0/VK7JNreaNeaTRXoKjPuU7/gvchOlmuzCpFzcRAK1zj/hqfPaEnvDL3BOip5Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:58:46.029950Z"},"content_sha256":"5078a485386dcbbbe23244b65285159c15912d1a6da69b3d306e657334ee324b","schema_version":"1.0","event_id":"sha256:5078a485386dcbbbe23244b65285159c15912d1a6da69b3d306e657334ee324b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:35IGKJUXVHTC24S5OCU37QIOTZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multi-Instantons and Exact Results III: Unified Description of the Resonances of Even and Odd Anharmonic Oscillators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A. Surzhykov, J. Zinn-Justin, U. D. Jentschura","submitted_at":"2010-01-22T03:31:30Z","abstract_excerpt":"This is the third article in a series of three papers on the resonance energy levels of anharmonic oscillators. Whereas the first two papers mainly dealt with double-well potentials and modifications thereof [see J. Zinn-Justin and U. D. Jentschura, Ann. Phys. (N.Y.) 313 (2004), pp. 197 and 269], we here focus on simple even and odd anharmonic oscillators for arbitrary magnitude and complex phase of the coupling parameter. A unification is achieved by the use of PT-symmetry inspired dispersion relations and generalized quantization conditions that include instanton configurations. Higher-order"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.3910","kind":"arxiv","version":2},"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":"2026-05-18T03:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0XzwgRD5nhopanUkfrfubJQ29kqHjLIbuDg1fu7tMvwm0lb5RWRhmf0NjwXZTKV3UakAvtuNQ0c3nDkUiMHyBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T10:58:46.030670Z"},"content_sha256":"3ec42ccc70e0d088544960d90616575fca11cafdcbe580812f6f8168260c42d1","schema_version":"1.0","event_id":"sha256:3ec42ccc70e0d088544960d90616575fca11cafdcbe580812f6f8168260c42d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/35IGKJUXVHTC24S5OCU37QIOTZ/bundle.json","state_url":"https://pith.science/pith/35IGKJUXVHTC24S5OCU37QIOTZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/35IGKJUXVHTC24S5OCU37QIOTZ/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":"2026-06-10T10:58:46Z","links":{"resolver":"https://pith.science/pith/35IGKJUXVHTC24S5OCU37QIOTZ","bundle":"https://pith.science/pith/35IGKJUXVHTC24S5OCU37QIOTZ/bundle.json","state":"https://pith.science/pith/35IGKJUXVHTC24S5OCU37QIOTZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/35IGKJUXVHTC24S5OCU37QIOTZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:35IGKJUXVHTC24S5OCU37QIOTZ","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":"8e126c9960fc9d8e037bafc8d4b88e6623b92f9cb8a38f2710650c6d283c97e0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-01-22T03:31:30Z","title_canon_sha256":"1f62a1488a4b7d2da803192de51d43cc73cd211d227615ab38c4beb2cbf370f4"},"schema_version":"1.0","source":{"id":"1001.3910","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.3910","created_at":"2026-05-18T03:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1001.3910v2","created_at":"2026-05-18T03:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.3910","created_at":"2026-05-18T03:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"35IGKJUXVHTC","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"35IGKJUXVHTC24S5","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"35IGKJUX","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:3ec42ccc70e0d088544960d90616575fca11cafdcbe580812f6f8168260c42d1","target":"graph","created_at":"2026-05-18T03:52:12Z","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":"This is the third article in a series of three papers on the resonance energy levels of anharmonic oscillators. Whereas the first two papers mainly dealt with double-well potentials and modifications thereof [see J. Zinn-Justin and U. D. Jentschura, Ann. Phys. (N.Y.) 313 (2004), pp. 197 and 269], we here focus on simple even and odd anharmonic oscillators for arbitrary magnitude and complex phase of the coupling parameter. A unification is achieved by the use of PT-symmetry inspired dispersion relations and generalized quantization conditions that include instanton configurations. Higher-order","authors_text":"A. Surzhykov, J. Zinn-Justin, U. D. Jentschura","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-01-22T03:31:30Z","title":"Multi-Instantons and Exact Results III: Unified Description of the Resonances of Even and Odd Anharmonic Oscillators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.3910","kind":"arxiv","version":2},"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":"sha256:5078a485386dcbbbe23244b65285159c15912d1a6da69b3d306e657334ee324b","target":"record","created_at":"2026-05-18T03:52:12Z","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":"8e126c9960fc9d8e037bafc8d4b88e6623b92f9cb8a38f2710650c6d283c97e0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-01-22T03:31:30Z","title_canon_sha256":"1f62a1488a4b7d2da803192de51d43cc73cd211d227615ab38c4beb2cbf370f4"},"schema_version":"1.0","source":{"id":"1001.3910","kind":"arxiv","version":2}},"canonical_sha256":"df50652697a9e62d725d70a9bfc10e9e44933cbd24cd5fadf208769a07b7ce94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df50652697a9e62d725d70a9bfc10e9e44933cbd24cd5fadf208769a07b7ce94","first_computed_at":"2026-05-18T03:52:12.672535Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:12.672535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fgDmGGVp+pDAqLEOCPntEBUfhXAGitUHqGdaVl1/fyil0YtH0p0ThqC75ms44LEiVUx1tMiwo/tCFmWoCQsHAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:12.673151Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.3910","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5078a485386dcbbbe23244b65285159c15912d1a6da69b3d306e657334ee324b","sha256:3ec42ccc70e0d088544960d90616575fca11cafdcbe580812f6f8168260c42d1"],"state_sha256":"2610eb71e2e41ee317dc7be95fa0b356e4ab946a0490336a263411e094dca34a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1D/ijgCxnbTxsCEtqZ8F5nrVd4QWtpXzfQbipvtL6hTZI45D8MFQZ1g8gsJCGkuoqtj2pJSrKLiXd6amdT4ACw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T10:58:46.035048Z","bundle_sha256":"18f7ca25cbfd4c52e448622780ee9a45abd9c019fc23df6f739607de244f4cf8"}}